Unit i Dc Corrected Version-lib

Regulation 2013 Academic year 2015-2016

IFET COLLEGE OF ENGINEERINGDEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

SUB CODE: EC6501 YEAR: IIISUBJECT: DIGITAL COMMUNICATION SEMESTER: V

UNIT I SAMPLING AND QUANDISATION

Syllabus:Low pass sampling – Aliasing- Signal Reconstruction-Quantization - Uniform & non-uniform quantization - quantization noise - Logarithmic Companding of speech signal- PCM - TDM

PART-A (2 MARKS)

Low Pass Sampling:1. What is meant by digital communication?

The digital communication systems the signal is transmitted and received in digital pulse of constant amplitude, frequency and phase. If noise or distortion occurs methods exist to determine that this as happened and appropriate action to correct the errors is taken which has occurred. The types of digital pulse modulation are PCM, DM, ADM and DPCM.

2. What are the elements of basic communication systems?The elements of basic communication systems is

Source – speech, video etc. Transmitter- conveys information. Channel - the physical medium between transmitter and receiver. Any device which

serves the purpose of linking transmitter with receiver can be called a channel, noise-undesirable signal.

Receiver-extracts information and user-utilize information.3. What is meant by sampling?

Sampling is the Conversion of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal)A sample is a value or set of values at a point in time and/or space. A sampler block takes an analog signal m(t) as the input and convents it to ms(t).

4. What is meant by encoding and decoding?.An encoder is a device, circuit, transducer, software program, algorithm or person that converts information from one format or code to another, for the purposes of standardization, speed, security, or saving space by shrinking size. A decoder is a device which does the reverse of an encoder, undoing the encoding so that the original information can be retrieved. The same method used to encode is usually just reversed in order to decode.

5. State sampling theorem. A/M’11, M/J’12A band limited signal having no spectral components above fm Hz can be determined uniquely by values sampled at uniform intervals of

Ts <1/2 fm secThis particular theorem is called uniform sampling theorem. From this one can state the Nyquist rate of sampling which gives the minimum sampling frequency needed to reconstruct the analog signal from sampled waveform.

fs > 2fm

6. State bandpass sampling theorem.The bandpass signal x(t) whose maximum bandwidth is 2W can be completely represented into and recovered from its samples. If it is sampled at the minimum rate of twice the bandwidth.

IFETCE/ECE/IIIYR/VSEM/EC2301-DIGITALCOMMUNICATION/UNIT-1/COMBINED VERSION/16MARKS QB/VER1.0

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Bandpass sampling is a technique where one samples a band pass-filtered signal at a sample rate below its Nyquist rate (twice the upper cut-off frequency), but is still able to reconstruct the signal.

7. What is meant by impulse sampling?Let us sample an analog waveform x(t) by a sequence of unit impulses (ie Dirac delta functions).We further assume that the spectrum of x(t) is band limited, it is zero outside the interval (-fm <f<fm).We sample x(t) at times t=nTs by a periodic train of delta functions x(t).In practical digital systems fs is always taken to be more than the nyquist rate ie;oversampled to help the filtering action.

8. What is natural sampling? M/J’13, N/D’13In natural sampling flat top rectangular pulses of finite width is used to sample the analog the analog waveform. This is done because the top of each pulse in the sampled sequences retains the shape of the original signal during that pulse interval. Therefore the spectrum of flat top pulse approaches the spectrum of impulse samples For Ts0.

9. Define the two different aspects of the sampling process.Quadrature sampling of a band pass signal, which involves sampling of the low pass in phase and quadrature components of the band pass signal in accordance with the sampling theorem.Sampling of a message process, which introduces a mean squared error that is zero when the process is strictly band limited and the sampling rate is twice the highest frequency component of the process.

10. Define Nyquist rate.The Nyquist rate is twice the bandwidth of a band limited function or a band limited channel. The Nyquist criterion is often stated as fs > 2W.Let the signal be band limited to W hertz. Then Nyquist rate is given as

Nyquist rate = 2W samples/secAliasing will not take place if sampling rate is greater than Nyquist rate.

11. Determine the Nyquist rate for V(t)=5cos(5000πt).cos2(8000πt).Solution:

12. What is meant by flat top sampling?

This is practically possible sampling method. The top of the samples remains constant and equal to instantaneous value of baseband signal x(t) at the start of sampling. The duration of each sample is T and sampling rate is equal to fs=1/Ts. Flat top sampling is also called as rectangular pulse sampling. Normally the width of the pulse in flat top sampling is increased as far as possible to reduce the transmission bandwidth.

13. Define aperture effect.By using flap top samples an amplitude distortion is introduced in reconstructed signal x(t) from s(t). The high frequency roll off of H(f) acts like a low pass filter and attenuates upper portion of message spectrum. These high frequencies of x(t) are affected. This effect is called aperture effect. During reconstruction an equalizer is required to compensate for this aperture effect.


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http://en.wikipedia.org/wiki/Bandlimited

http://en.wikipedia.org/wiki/Bandwidth_(signal_processing)

http://en.wikipedia.org/wiki/Nyquist_rate

http://en.wikipedia.org/wiki/Sample_rate

http://en.wikipedia.org/wiki/Bandpass

http://en.wikipedia.org/wiki/Sampling_(signal_processing)


14. List out the steps required in A/D conversion for under sampling. The signal passes through a high performance analog low pass antialiasing filter to

limit its bandwidth. The filtered signal is sampled at the Nyquist rate for the approximately bandlimited

signal. The samples are processed by analog to digital converter that maps the continuous

valued samples to a finite list of discrete output levels.15. What are the steps required in A/D conversion without oversampling?

The signal passes through a high performance analog lowpass antialiasing filter to limit the bandwidth.

The filtered signal is sampled at the Nyquist rate for the approximately bandlimited signal obtained in previous step.

The samples are processed by an analog-to-digital converter that maps the continuous valued samples to a finite list of discrete output levels.

16. What are the steps required in A/D conversion for oversampling? The signal passes through a low performance analog lowpass filter (prefilter) to limit

its bandwidth. The pre filtered signal is oversampled at a much higher sampling rate than the Nyquist

rate for the band limited signal. The samples are processed by analog to digital converter that maps the continuous

valued samples to a finite list of discrete output levels. The digital samples are then processed by high performance low cost digital filter to

reduce the bandwidth.17. Why is pre-filtering done before sampling? N/D’10

The signal must be limited to some highest frequency W Hz before sampling. Then the signal is sampled at the frequency of fs = 2W or higher.

Hence the signal should be pre-filtered (low pass filtered) to eliminate any frequency components higher than W Hz.

If the signal is not pre-filtered, then frequency components higher than W Hz will generate aliasing in the sampled signal spectrum.

Aliasing:

18. What is meant by foldover?Foldover which is also referred as Aliasing, which is refers to some portions of the frequency shifted replicas of the spectrum of the analog signal folding over inside the desired spectrum.Aliasing arises because a analog signal cannot be limited in both time and frequency simultaneously.The recipe for controlling its effect involves the use of pre-alias filter, combined with the choice of a sampling rate in excess of the Nyquist rate.

19. What is anti-aliasing filter?There are two ways by which the problem of aliasing can be tackled; both of these methods make use of antialiasing filters. In pre-filtering antialiasing filter, the analog signal itself is pre-filtered so that new maximum frequency is reduced to fs/2. In post fltering antialiasing filter, aliased terms are eliminated after sampling with help of LPF operating on the sampled data. The cutoff frequency needs to be less than (fs-fm).

20. What is meant by aliasing effect?Aliasing effect takes place when sampling frequency is less than Nyquist rate. Under such condition, the spectrum of the sampled signal overlaps with itself. Hence higher frequencies take the form of lower frequencies. This interference of the frequency


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components is called aliasing effect. Aliasing can also occur in spatially sampled signals, for instance digital images.

21. What are the corrective measures to combat the effects of aliasing? To combat the effects of aliasing in practice we may use two corrective measures,Prior

to sampling, a low pass pre-alias filter is used to attenuate those high frequency components of the signal that are not essential to the information being conveyed by the channel.

The filtered signal is sampled at a rate slightly higher than the Nyquist rate.22. Sketch the schematic which shows the aliasing problem in the frequency domain.

Figure: Aliasing: The spectral Representation, (a) Signal (b) Sampled Signal

Signal Reconstruction:23. Draw the schematic for signal reconstruction scheme.

Sample and hold circuits-A sample and hold (S/H) circuit is an analog device that samples the voltage of a continuously varying analog signal and holds its value at a constant level for a specified minimum period of time.Low Pass Filter-Allows the low frequency components.Equalizer-Used to adjust the balance between the frequency components of the signal.

24. What is meant by sample and hold circuits?A sample and hold (S/H) circuit is an analog device that samples the voltage of a continuously varying analog signal and holds its value at a constant level for a specified minimum period of time. Sample and hold circuits and related peak detectors are the elementary analog memory devices. They are typically used in analog-to-digital converters to eliminate variations in input signal that can corrupt the conversion process.

25. Define transition bandwidth.All realizable filters require a non zero bandwidth for the transition between the pass band and stop band, commonly known as transition bandwidth. Filter complexity and cost rise sharply with narrower transition bandwidth. However if we want to keep the sample rate down, we should go for a very narrow transition bandwidth. Trade off is required in the sampler implementation.

26. What is need of trade off in sampler implementation?Tradeoff is required between the cost of a small transition bandwidth and cost of higher sampling rate ( ie cost of more storage and higher transmission rate). In many systems the rule of thumb is to make the transition bandwidth between 10% and 20% of the signal bandwidth. If we account for the 20% transition bandwidth of the antialiasing filter we have a practical Nyquist rate fs > 2.2 fm.


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Analog Waveform

EqualizerLow-Pass Filter

Sample and Hold

Circuit

Sampled Waveform

http://en.wikipedia.org/wiki/Analog-to-digital_converter

http://en.wikipedia.org/wiki/Memory

http://en.wikipedia.org/wiki/Precision_rectifier#Peak_detector

http://en.wikipedia.org/wiki/Analog_signal

http://en.wikipedia.org/wiki/Voltage

http://en.wikipedia.org/wiki/Analog_circuit

http://en.wikipedia.org/wiki/Analog_signal

http://en.wikipedia.org/wiki/Voltage

http://en.wikipedia.org/wiki/Analog_circuit

http://en.wikipedia.org/wiki/Digital_image


27. What should be the pass band for antialiasing and smoothing filters used with pulse modulation/demodulation systems? Antialiasing filter used before sampling. It should band limit the signal to maximum

signal frequency of W Hz. Hence its pass band should be W Hz. Smoothing filter is used after reconstruction or interpolation. It should successfully

pass all the frequencies of 0 and W Hz and block frequencies greater than W Hz.

Quantization28. What is meant by quantization? M/J’12

The conversion of analog signal value into digital signal value. The analog value is assigned to the nearest digital value. This is called quantization. The quantized value is then converted to equivalent binary value. The quantization levels are fixed depending upon the number of bits. Quantization is performed in every analog to digital conversion. There are two types such as Uniform and non uniform quantization.

29. What is quantile interval?The quantized levels may assume positive and negative values. The step size between quantization levels, called quantile interval, is denoted by q volts. The maximum errors in this approximation is limited to half of the quantile interval i.e., q/2 volts. So if the signal at a larger stage, gets contaminated with the channel noise, then as long as the instantaneous noise voltage is less than q/2 volts it would have no effect on the signal. This suggests that large step size improves the noise immunity.

30. What is quantization error? A/M’11In source coding (analog to digital conversion and compression), the difference between the actual value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or functions. The error signal is sometimes considered as an additional random signal called quantization noise because of its stochastic behavior.

31. What is the Requirement for Fine Quantization?For fine quandization ,the quantized signal power can be approximated to the second moment of the clean signal(t).

And the quandization power is

Where m2

p is the peak quandization level of the uniform quandiser.so if we denote the SNR for quandisation alone as (S/N)q then we can write

Uniform & non-uniform quantization:

32. What is uniform quantization?When the quantization levels are uniformly distributed over the full range, the quantiser is called an uniform quantiser. Each sample value of the analog waveform is approximated to a quantization level. The maximum errors in this approximation is limited to half of the quantile interval i.e., q/2 volts. It is observed that SNR improves as we increase the number of quantization levels. In the limits when L is very high quantization SNR become infinite.

33. List the types of uniform quantization. Midtread quantizer –Mid-tread quantizers do have a zero output level, and can reach

arbitrarily low bit rates per sample for input distributions that are symmetric and taper off at higher magnitudes.


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Midriser quantiser –Mid-riser uniform quantizers do not have a zero output value their minimum output magnitude is half the step size. Mid-riser quantizers also always produce an output entropy of at least 1 bit per sample.

Biased quantiser –Midriser and Midtread quantizers are rounding quantizers. But biased quantizer is truncation quantizer.

34. What is non-uniform quantization?Quantization noise depends upon step size. In non-uniform quantization the step size is not fixed. It varies according to certain law or as per input signal amplitude. It effect is to improve the overall SNR by reducing the quantizing noise for the predominantly weak signals at the expense of an increase in quantization noise for the rarely occurring strong signals.

35. State any two non-uniform quantization rules. M/J’13 The step size is small at low input signal level. Hence quantization error is also small

at these inputs. Therefore signal quantization noise power ratio is improved at low signal levels.

The step size is higher at high input signals. Hence signal to noise ration remains almost same throughout the dynamic range of quantiser.

36. Compare uniform and non-uniform quantization. N/D’11Uniform quantization – When the quantization levels are uniformly distributed over the full range, the quantiser is called a uniform quantiser.Non uniform quantization – Quantization noise depends upon step size. In non-uniform quantization the step size is not fixed. It varies according to certain law or as per input signal amplitude.

37. What is the need for non-uniform quantization of speech signal?In uniform quantization the quantiser has a linear characteristic. The step size also remains same throughout the range of quantizer. Therefore over the complete range of inputs, the maximum quantization error also remains same. Maximum quantization error will be occurs due to uniform quantization. SNR for large crest factor signal will be very less so speech and music should use non uniform quantization.

38. Define crest factor.Crest factor describes how strong the signal peak value is with respect to its rms value.

Crest factor = peak value / rms value.Speech has a high crest factor. So if uniform quantisers are used for speech, most of the time the quantiser slope will be more than signal slope.

39. Mention the use of adaptive quantizer in adaptive digital waveform coding schemes.Adaptive quantiser changes its step size according to variance of the input signal. Hence quantization error is significantly reduced due to adaptive quantization. ADPCM uses adaptive quantization. The bit rate of such schemes is reduced due to adaptive quantization. Adaptive quantisers are two types such as adaptive quantization with forward estimation (AQF) and adaptive quantization with backward estimation (AQB).

40. What do you understand from adaptive coding?In adaptive coding the quantization step size and prediction filter coefficients are changed as per properties of input signal. This reduces the quantization error and number of bits used to represent the sample value. Adaptive coding is used for speech coding at low bit rates. It refers to variants of entropy encoding methods of lossless data compression


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http://en.wikipedia.org/wiki/Lossless_data_compression

http://en.wikipedia.org/wiki/Entropy_encoding

http://en.wikipedia.org/wiki/Entropy_(information_theory)


Quantization noise41. Define quantization noise.

When the signal is converted from analog to digital form, the analog sample amplitude is assigned the nearest available quantization amplitude level. The difference between quantized value and actual value of the sample introduces permanent distortion in the signal. It is called quantization error or quantization noise. Quantization noise, Є = xq(nTs) – x(nTs). xq(nTs) is quantized value of sample and x(nTs) is actual value of sample.

42. Draw the conceptual model for evaluating signal-to-noise ratio.

43. What is quantization noise power? N/D’10Quantization noise power is the noise power due to quantization noise. Let the quantization noise has the pdf of f (Є). Mean squared error is also called the quantization noise power. Adding one bit to the quantizer halves the value, which reduces the noise power by the factor ¼. Finally the quantization noise power is given by e2

q = q2/12 where q will be in size of quantile interval

44. What is known as Additive White Gaussian Noise (AWGN)?Electrical Noise is produced by varied sources such as galactic and atmospheric noise, switching transients, inter-modulation noise, and random motion of electrons in a communication system etc. Except thermal noise, most other noises can be eliminated. Thermal noise is generally modeled as Additive, White, Gaussian Noise (AWGN).It has zero mean and a constant double-sided power spectral density of ɳ/2,for all frequencies from –α to + α.

45. A continuous time signal is sampled and then transmitted as a PCM signal with polar NRZ format. Assume the quantization noise to be Gaussian with zero mean and its variance at the matched filter input is 0.05 volts2.If the channel noise increases and as a result the error rate increases to 1 in 104.What is the variance of the channel noise?Solution:The noise is now sum of quantization and channel noise.


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46. A signal m (t) is uniformly distributed in the range ±Vp .The signal is quantized by an uniform quantiser.Evaluate the ratio of the peak SNR to the average SNR for the quantized signal.The Noise power is always calculated on average basis. For uniform quandisation,the quantization noise power is

Peak signal value is ±Vp.So Peak signal Power is Sp=V2p.Hence,Peak SNR is

The Pdf of m(t) is uniform

So the average signal power Sav equals the 2nd moment of m(t)

Hence the average SNR is

So the peak SNR is 3 times the average SNR.47. A continuous time signal is sampled and then transmitted as a PCM signal with polar

NRZ format. Assume the quantization noise to be Gaussian with zero mean and its variance at the matched filter input is 0.01 volts2.If the system is operated above threshold. Determine the pulse amplitude that must be transmitted for the average error rate not to exceed 1 in 108 bits.Solution:The noise here is only quantization .Above threshold of PCM no channel noise is present

48. What are the two types of quantization errors that occur in delta modulation?

Slope overload error: The step size of quantization is not enough to follow the large changes in input signal. Hence there is difference between approximated signal and input signal.

Granular noise: The step size is too large; hence approximated signal cannot follow the small variations in input signal. For every small variation in input signal, there is large change in approximated signal. It is also called as hunting.


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49. The information in an analog waveform, with maximum frequency content of 3kHz, is to be transmitted over an M-ary PCM system, where the number of pulse levels is M=16.The quantization error is specified not to exceed ±1% of the peak-to-peak analog signal. What is the minimum number of bits/sample that should be used in digitizing the analog waveform?Solution: The relation between the tolerance in quantization error and PCM word size is obtained as

To Meet distortion requirement, we take l=6 bits/sample50. Draw the transfer characteristics of quantizer.

51. The information in an analog waveform, with maximum frequency content of 3kHz, is to be transmitted over an M-ary PCM system, where the number of pulse levels is M=16.The quantization error is specified not to exceed ±1% of the peak-to-peak analog signal. i) What is the minimum sampling Rate and what is the resulting bit transmission rate?ii) What is the Baud rate of the system?Solution:i) Minimum Sampling Rate fs=Nyquist Rate=2x3=6 K samples/sec.

The resulting bit transmission rate=l x fs=36kbpsii) 2k=16=>k=4,So,the binary stream will be partitioned into symbols each of which

contain 4 bits. This implies that the line coder should have a repertoire of 16 analog waveforms.

52. What is slope overload error?

When the distortion arises because of the large dynamic range of the input signal. The step size of quantization is not enough to follow the large changes in input signal. Hence there is difference between approximated signal and input signal. It is called as slope overload error. To reduce this error step size should be increased when slope of signal of x(t) is high. It is also called as startup error.

53. Define pre-emphasis and de-emphasis.Pre-emphasis refers to a system process designed to increase the magnitude of some frequencies with respect to the magnitude of other frequencies in order to improve the overall signal-to-noise ratio by minimizing the adverse effects of such phenomena as


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attenuation distortion or saturation of recording media in subsequent parts of the system. The mirror operation is called de-emphasis, and the system as a whole is called emphasis.

Logarithmic Companding of speech signal:

54. What is meant by Companding?To avoid granular noise signals need to have tapered quantizing levels.(ie:step size is smaller for smaller signals and larger for larger signals).A quantiser with varying step-size is difficult to implement. A more practical approach is to predistort the signal by a logarithmic compression characteristic and then put it to a uniform quantiser.This compressed and quantized signal is transmitted through the channel and can be undistorted at the receiver by the same algorithm. This process is known as companding.

55. Define µ law compander.µ-law for positive amplitude signal is

where, mp is the peak amplitude value that the quantiser.µ-law is primarily used in 8-bit PCM digital telecommunication systems in North America and Japan. µ law transfer function are logarithmic and have odd symmetry.56. Define a law compander. N/D’13

An A-law algorithm is a standard companding algorithm, used in 8-bit PCM digital communication systems to optimize, modify, the dynamic range of an analog signal for digitizing. A-law positive amplitude is

Draw the diagram which shows the variation of signal to noise ratio with respect to

signal level with and without companding.

57. What are the types of analog encoders?Analog encoders used for encoding speech and images. There are three types of analog encoders. Temporal waveform coding – encoder captures temporal characteristics of source

waveforms. Spectral waveform coding – signal waveform is usually divided into different

frequency bands. Model based coding – based on mathematical modeling of the source.


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http://en.wikipedia.org/wiki/Japan

http://en.wikipedia.org/wiki/North_America

http://en.wikipedia.org/wiki/Telecommunication

http://en.wikipedia.org/wiki/Digital_data

http://en.wikipedia.org/wiki/PCM

http://en.wikipedia.org/wiki/Clipping_(audio)

http://en.wikipedia.org/wiki/Attenuation_distortion


58. What is temporal waveform coding? N/D’11A speech or an image source produces signals that vary with time. If we are to digitize the signals coming out of such a source, we need to digitize some time varying parameter of the time-waveform representing the source. This process is known as temporal waveform coding. Examples are transducers used in process control for the measurements of temperature, pressure, velocity, flow rates, etc.

59. What is spectral waveform coding?The spectral waveform coding, coding is done by decomposing the signal in various frequency subbands and separately encoding the signal in each sub band. The encoding is done at each subband by waveform encoding technique only, which can be either on the time domain waveforms in each sub band or on the frequency domain of the corresponding time domain in each sub band.

60. What is model based coding?The aim of model based coding techniques is to characterize the signal in terms of its various parameters and then encode those parameters, not the signal. The decoder at the receiver, after obtaining the encoded parameter values, synthesizes the signal from those parameters. For estimating its parameters, a signal need to be observed over an interval of time during which its statistical properties do not change.

61. What is meant by transducers?A transducer is a device that converts a signal in one form of energy to another form of energy. Energy types include electrical, mechanical, electromagnetic, chemical, acoustic and thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a transducer. It is widely used in measuring instruments.

62. What is spatial waveform with example?The spatial waveform is defined as function of one or more spatial variables (e.g displacement in x and y) it often converted to time-varying waveform by a scanning operation, and done in facsimile transmission. An example of spatial waveform is single images, such as a photograph, or moving images, such as successive images of moving picture film.

PCM:63. What are the essential operations in the transmitter of PCM?

The essential operations in the transmitter of a PCM system are1. Sampling2. Quantizing3. Encoding

The sampling, quantizing and encoding operations are usually performed in the same circuit, which is called an analog to digital converter. Regeneration of impaired signals occurs at intermediate points along with the transmission path.

64. What is Pulse coded modulation (PCM)?If a PAM signal is first quantized and then converted to a digital code, we get a complete digital signal. This signal is called pulse coded modulated signal and the process is known as pulse coded modulation (PCM). The advantages of PCM are high noise immunity, used for storage systems (CD recording, hard disk recording), used for baseband transmission of the signal


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65. Draw the block diagram of PCM.TRANSMITTER

RECEIVER

66. What are the advantages of PCM over analog Pulse modulation?The advantages of PCM over analog pulse modulation method is that in PCM, the information does not lie in any property of the pulse waveform, rather it lies in the presence or absence of the pulse or to which side of a threshold value the pulse amplitude lies.Thus, the noise immunity of a PCM signal is much more than any analog pulse modulation signal. Therefore, PCM can be used for storage systems.

67. What is meant by PCM word size?For digital telephone channels, each speech sample is PCM encoded using 8 bits, yielding 28 or 256 level per sample. The choice of the number of levels of bits per sample depends on how much quantization noise we are willing to tolerate with the PCM format. The relation between the tolerance in quantization error and PCM word size is obtained as

68. What is meant by holding circuit?

The holding circuit may be a zero-order hold circuit which is nothing but a switch opening and closing to a capacitor.The capacitor retains the value of the previous samples till a new pulse arrives. This is followed by a second order low pass filter to produce the desired analog signal at the receiver output.

69. What is meant by regenerative repeaters?Digital repeaters are also called as regenerative repeaters. In practical long haul communications systems a link usually runs for several hundred kilometers and to overcome signal losses over such a long path, the signal is boosted at intermediate stations called repeaters. Each repeater consist of both transmitter and receiver block. So baseband signal power requirement is 9.27dB less for regenerative repeaters.

70. Draw the block diagram of a regenerative Repeater?


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ENCODER QUANTISER SAMPLER

LPFHOLDING CIRCUIT DECODERQUANTISER

Regenerated PCM Wave

Distorted PCM Wave

Decision Making Device

Timing Circuit

Amplifier Equalizer


71. A telephone signal band limited to 4 kHz is to be transmitted by PCM.The signal to quantization noise is to be at least 40dB.Find the number of levels into which the signal is to be encoded. Find the BW required for transmission.Solution:

72. A PCM system uses a uniform quantizer followed by a7 bit binary encoder.The bit rate of system is 50x106 bits/sec.What is the maximum message BW for which the system operates satisfactorily. What is the SNR for a full load sinusoidal signal?Solution:

73. Define idle channel noise.

Idle channel noise is the coding noise measured at the receiver output with zero transmitter input. The zero input condition arises during silences in speech. The average power of this form of noise depends on the type of quantizer used. In a quantizer of the midriser type, zero input amplitude is encoded into one of the two inner most representations levels and these two levels are equiprobable; the idle channel noise for midriser quantizer has zero mean and an average power of ∆2/4.

74. What is the SNR of PCM system if number of quantization levels is 28?

75. Define baud rate.

The baud rate of a data communications system is the number of symbols per second transferred. A symbol may have more than two states, so it may represent more than one binary bit (a binary bit always represents exactly two states).Therefore the baud rate may not equal to the bit rate, especially in the case of recent modems, which can have (for example) up to nine bits per symbol.


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76. What is meant by PCM bandwidth?PCM bandwidth of any signal to determine we need to find its frequency domain representation.PCM signal is quantized and encoded PAM signal. The bandwidth of any digital signal depends on both symbol rate and pulse shape.The least transmission bandwidth of PCM system in terms of signal bandwidth is

BT PCM ≥ lB 77. What are the noises present in PCM systems?

There are several noise and interference in a PCM system. Such as Aliasing noise -due to improper sampling Quantization noise –occurs in transmitter itself Channel noise – occurs outside the transmitter and cannot follow any deterministic

pattern. Inter symbol interference – due to high data transmission rate.

78. A signal m1 is band limited to 5kHz and 3 other signals m2 and m3 and m4 each band limited to 4 kHz are time multiplexed and fed to a PCM encoded having 1024 quantization levels. Find the bit rate of PCM and also BW required for transmission.Solution:

fs

M1 5kHz 10kHzM2 4kHz 8kHzM3 4kHz 8kHzM4 4kHz 8kHz

34 kHz = 34000 samples/secM=1024=2N

N=10Number of bits generated per second =34x103x10

=34x104 bits/sec=340 kbps

Theoretical minimum BW:

79. Draw the diagram which shows the compander characteristics of a PCM channel.

80. What is threshold effect of PCM?The SNR stabilizes after a minimum baseband SNRγb is reached. This minimum is called threshold γb and it depends on the PCM word length (l).The SNR curve becomes horizontal when the baseband SNR crosses the threshold value.


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This explains that for large γb, argument of Q is so large that its value is nearly zero.

81. What is saturation effect of PCM?The horizontal portion of the graph is called Saturation Region. The saturation region of the system noise is entirely quantization noise. Hence the SNR of a saturated PCM system can be written as

Expressing SNR of the saturated PCM system in dB scale

82. What is the SNR of the companded signal?

The SNR of the companded signal becomes,

Where x is the random variable distributed in the range (-1,1).the value of <<1 and

<<1.83. A compact disc (CD) recording system samples signals with 16bit A/D converter at

44.1 ksamples/sec and converts them to PCM Form.(a) Determine the output signal to noise ratio for a full scale sinusoid.(b) If the recorded music is designed to have a crest factor of 20, determine the

average output SNR.(c) The bit stream of digitized data is augmented by error correcting codes, clock

extraction bits and display and control bits so that the overhead becomes 100%.Determine the output bit rate of the CD recorder system.

(d) A CD can record an hour’s worth of music. Determine the number of bits recorded on the CD.


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84. Write the expression by clubbing the SNR expression for uncompanded and

companded PCM.Solution:By clubbing the SNR expressions for uncompanded and companded PCM we can write.

The transmission bandwidth of a sync shaped PCM signal derived from an analog signal of bandwidth B is IB. So SNR of a PCM signal in terms of its transmission bandwidth can be written as,

Where the factor

is called the bandwidth expansion factor.85. What is adaptive pulse coded modulation (APCM)?

Adaptive pulse code modulation is a technique where the quantization noise is reduced by using an adaptive quantiser. It can be performed by many ways; one such way is use a uniform quantiser that varies its step size in accordance with the variance of the past signal samples. APCM efficiency can be improved by allowing the system to adapt to the slowly time-varying statistics of the source.


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86. How the quantization noise can be reduced in adaptive PCM?Quantization noise in APCM is reduced by using an adaptive quantiser. This can be done in many ways; however a particularly simple way is to use a uniform quantiser that varies its step size in accordance with the variance of the past signal samples. In its simplest form the algorithm for the step size adjustment employs only the previous signal sample.

87. What is meant by quadrature mirror filter (QMF)?Quadrature mirror filter (QMF), it can deliver an alias-free response due to its perfect reconstruction property. By using QMFs in subband coding, the lower frequency band is repeatedly subdivided into factors of two and then the output is decimated by a factor of two to reduce the sampling rate by half. Generally SBC is implemented by QMF.

88. What is wavelet processing?QMF filters are implemented as digital filters and now the technique is called wavelet processing. With processing, much flexibility can be achieved for decomposing the signal as well as encoding it. So, the overall bit rate needed to transmit a wavelet processed signal reduces drastically and in recent times it is mostly preferred technique.

89. What are the major subdivision of analog encoders used for encoding speech and image?The analog encoders are used for encoding speech and images. They are broadly subdivided into three categories.1.) Temporal waveform coding: The encoder captures the temporal characteristics of the

source waveform.2.) Spectral waveform coding: The signal waveform is usually subdivided here into

different frequency bands, and either the time waveform in each band or its spectral characteristics are encoded for transmission.

3.) Model based coding; It is based on a mathematical modeling of the source, there by capturing the source statistics.

90. What is meant by model based encoding?The aim of model based encoding is to characterize the signal in terms of its various parameters and then encode those parameters, not the signal. The decoder at the receiver after obtaining the encoded parameter values, synthesizes the signal from those parameters. The advantage of this encoding is the number of bits needed for encoding the parameters is substantially lower than that needed for encoding the signal.

91. Differentiate the principles of temporal waveform and model based coding. M/J’13Temporal waveform: Time domain waveform is encoded. Bit allocation depends upon time domain features. Reconstructed signal is near natural quality.Model based coding: Features/parameters of the signal are encoded. Bit allocation depends upon features or parameters of the signal. Reconstructed signal is synthetic (robotic).

92. Compare the speech encoding methods.Encoding method

Quantizer Coder(bits) Transmission rate(kbps)

CM Linear 12 96CM logarithmic 7-8 56-64DPCM logarithmic 4-6 32-48ADPCM adaptive 3-4 24-32DM binary 1 32-64ADM Adaptive binary 1 16-32


17


93. Compare the digital pulse modulation methods.parameter PCM DM ADM DPCMNumber of bits 4,8 or 16 bits

per sampleOnly one bit for one sample

One bit is used toencode one sample

Bits can be more than one but less than PCM

SNR good Poor Better than DM Fairapplications Audio and

video telephony

Speech and images

Speech and images

Speech and video

94. Design a counting quantizer for a 5 bit PCM with a voice signal as the input.Assume that the voice signal has a maximum frequency of 5kHz.Choose all parameters values and justify it.Solution:

fm=5kHzfs =10kHz

Let the ramp slope be 106 V/Sec,Input signal ranges from +10V to -10V,To reach 10V, ramp will take 10 sec=0.01m secThe conversation should be completed within 0.01m sec.For a 5bit converter, the duration of each state of counter

95. What is Pulse Amplitude Modulation?

In pulse amplitude modulation (PAM), the amplitude of a carrier consisting of a periodic train of rectangular pulses is varied in proportion to sample values of a message signal. In this type of modulation, the pulse duration is held constant.By making the amplitude if each rectangular pule the same as the value of the message signal at the leading edge of the pulse, the PAM so defined is exactly the same as flat top sampling.

TDM:96. Define Time Division Multiplexing (TDM).

Time-division multiplexing (TDM) is a method of putting multiple data streams in a single signal by separating the signal into many segments, each having a very short duration. Each individual data stream is reassembled at the receiving end based on the timing. TDM can be further extended into the time division multiple access (TDMA) scheme, where several stations connected to the same physical medium.


18


97. Sketch the waveforms illustrating TDM for two message signals.

98. How TDM is obtained from PAM?An important feature of pulse amplitude modulation is a conservation of time. So for a given message signal, transmission of the associated PAM wave engages the communication channel for only a fraction of the sampling interval on a periodic basis. Hence some of the time interval between adjacent pulse of the PAM wave is cleared for use by other independent message signals on time shared basis.This system is known as the time division multiplexing, which enables the joint utilization of a common channel by a plurality of independent message signals without mutual interference.

99. Write the function of commutator in TDM.The function of the commutator is two-fold,

1.) To take a narrow sample of each of the N input messages at a rate fs, that is slightly higher than 2W, where W is the cut off frequency of the pre-alias fliter.

2.) To sequentially interleave these N samples inside a sampling interval Ts=1/fs.This function is the essence of the time division multiplexing operation.

100.Draw the block Diagram for Time Division Multiplexing.


19


PART-B (16 MARKS)Low pass sampling:1. State Sampling theorem and explain the types of sampling techniques. M/J’12 (16)

(page no:184-186)Sampling theorem: A band limited signal having no spectral components above fm Hz can be determined uniquely by values sampled at uniform intervals of


fs > 2fm

Impulse sampling: Let us sample an analog waveform x(t) by a sequence of unit impulses (ie dirac delta functions). We further assume that the spectrum of x(t) is bandlimited, it si zero outside the interval ( - fm < f < fm) . we sample x(t) at times t=nTs by a periodic train of delta functions x(t). Natural sampling: In natural sampling flat top rectangular pulses of finite width is used to sample the analog the analog waveform. This is done because the top of each pulse in the sampled sequences retains the shape of the original signal during that pulse interval.

For Ts --->0.Aperture effect: The high frequency roll off of H(f) acts like a low pass filter and attenuates upper portion of message spectrum. These high frequencies of x(t) are affected. Transition bandwidth: All realizable filters require a non zero bandwidth for the transition between the pass band and stop band, commonly known as transition bandwidth. Sampler implementation:Without oversampling:

The signal passes through a high performance analog lowpass antialiasing filter to limit its bandwidth.

The filtered signal is sampled at the Nyquist rate for the approximately band limited signal.

The samples are processed by analog to digital converter that maps the continuous valued samples to a finite list of discrete output levels.

With over sampling: The signal passes through a low performance analog lowpass filter (prefilter) to limit its

bandwidth. The pre filtered signal is oversampled at a much higher sampling rate than the Nyquist

rate for the band limited signal. The samples are processed by analog to digital converter that maps the continuous

valued samples to a finite list of discrete output levels. The digital samples are then processed by high performance low cost digital filter to

reduce the bandwidth.

2. State and prove Sampling Theorem. (page no:187-189) (16)


20


Sampling theorem: A band limited signal having no spectral components above fm Hz can be determined uniquely by values sampled at uniform intervals of


fs > 2fm

Consider an analog signal g(t) that is continuous in both time and amplitude.Assume that g(t) has infinite duration but finite energy.

Let the sample values of the signal g(t) at times t=0,±Ts, ±2Ts,…… be denoted by the series {g(nTs),n=0,±1, ±2,…..},where Ts as the sampling period and fs=1/ Ts as the sampling rate.

Discrete time signal,∑n=−α

α

g (nT s )δ ( t−nT s )

Definition of delta function g(nT s ) δ ( t−nT s )=g( t ) δ ( t−nT s )

gδ(t)=g(t)δTs(t)where δTs(t) is called Dirac comb or ideal sampling function.Let G(f) and Gδ(f) denotes the Fourier transforms of g(t) and gδ(t) respectively.The convolution of G(f) and δ(f-mfs) equals G(f- mfs).Hence

Gδ(f) =

f s ∑m=−α

α

G( f−f s )

Gδ(f) =∑m=−α

α

g( n2W )exp(− jπ nfW )

G(f)=

12W

∑m=−α

α

g ( n2W )exp(− jπ nfW ) −W <f <W

Therefore if the sample values g(n/2W) of the signal g(t) are specified for all time, then the Fourier transform G(f) of the signal is uniquely determined by using the Fourier series. Because g(t) is related to G(f) by the inverse Fourier transform, it follows that the signal g(t) is itself uniquely determined by the sample values g(n/2W) for -∞ ≤n≤∞.in other words the sequence{g(n/2W)} contains all of the information of g(t).

Signal Reconstruction:3. (a) A television signal has a bandwidth of 4.5 MHZ. This signal is sample, quantized and

binary Coded to obtain PCM signal. Determine the sampling rate if the signal is to be sampled at the rate 20% above Nyguist rate. If the samples are quantized into 1024 levels, determine the number of binary pulses required to encode each sample. Determine the binary pulse rate of the binary coded signal and minimum bandwidth required to transmit this signal. N/D’11 (8)

Solution:


21


3.(b) Obtain an interpolation formula for reconstructing the original signal from the

sequence of samples. (8)(Or)

Explain the signal reconstruction from its sampled version.

Let as consider the signal g(t) and the sequence of samples {g(n/2W)}.The Fourier transform defining g(t) in terms of G(f),we get

g( t )=∫−∞

∞

G( f )exp( j 2π ft )df

=∫−W

W12W

∑−∞

∞g (n2W )exp(− jπ nfW )exp( j2 π ft )df

Interchanging the order of summation and integration

g( t )= ∑n=−∞

∞g (n2W )12W ∫

−W

W

exp[ jπ nf (t−n2W )]dfg( t )= ∑

n=−∞

∞g (n2W )sin (2πWt−nπ )

(2πWt−nπ )

sin cx=sin( πx )πx

Where x is an independent variable, The sinc function exhibits an important property known as the interpolatory property, which is given as

sin cx=¿ {1 x=0¿ ¿¿¿g( t )= ∑

n=−∞

∞g ( n2W )sin c (2Wt−n )


22


This equation provides an interpolation formula for reconstructing the original signal g(t) from the sequence of sample values {g(n/2W)},with the sinc function sinc(2Wt) playing the role of an interpolation function. Each sample is multiplied by a delayed version of the interpolation function and all the resulting waveforms are added to obtain g(t).

Aliasing:4.(a) What is aliasing? Derive the expression for the upper bound of aliasing error. (8) (page no:194-196)

The phenomenon of a high frequency in the spectrum of the original signal g(t) seemingly taking on the identity of a lower frequency in the spectrum of the sampled signal g(t) is called aliasing or fold over.Bound on aliasing Error:Let {g(n/fs)} denote the sequence obtained by sampling an arbitrary signal g(t) at the rate fs

samples per second.Let gi(t) denote the signal reconstructed from this sequence by interpolation, that is

gi( t )= ∑n=−∞

∞

g ( nf s )sin c ( f s t−n )Ε=|g(t)-gi(t)|

This is called Aliasing ErrorThe poisson’s formula is given as

∑m=∞

∞

G( f−mf s)=1f s

∑n=−∞

∞

g( nf s )exp (− j 2π nff s )

We can write the aliasing error as

ε=| ∑m=−∞

∞

[1−exp(− j2π mf s t ] ∫(m−1/2) f s

(m+1 /2 )f s

G( f )exp ( j 2π ft )df|

We can now derive the desired bound on the aliasing error ε by combining the following observations The term corresponding to m=0 vanishes The absolute value of the sum of a set of terms is less than or equal to the sum of the absolute values of the individual terms. The absolute value of the term 1-exp (-j2πmfst) is less than or equal to 2. The absolute value of the integral is bounded as

|G( f ) ∫(m−1/2) f s

(m+1 /2 )f s

G( f )exp ( j 2π ft )df|¿ ∫(m−1 /2 )f s

(m+1/2) f s

|G( f )|df

Thus the aliasing error is bounded as

ε≤ ∫|f|>f s /2

|G( f )|df


23


4.b) Explain briefly about the signal recovery using sample and hold circuit. (8)(page no:187-188)

The sampling process takes the form of natural sampling or flat-top sampling. In both cases the spectrum of the sampled signal is scaled by the ratio T/Ts, where T is the sampling pulse duration and Ts is the sampling period.

This ratio is quite small with the result that the signal power at the output of the low-pass reconstruction filter in the receiver is correspondingly small.

This situation can be eliminated by the use of amplification which can be quite large. A more attractive approach that is used for this is a simple sample and hold circuit. The circuit given below consists of an amplifier of unity gain and low output

impedance a switch and a capacitor it is assumed that the load impedance is large. The switch is timed to close only for small duration T of each sampling pulse, during

which time the capacitor rapidly charges up to a voltage level equal to that of the input sample.

When the switch is open the capacitor retains its voltage level until the next closure of the switch.

Thus the sample and hold circuit in its ideal form produces an output waveform that represents a staircase interpolation of the original analog signal as illustrated in the figure.

In flat top sampling we deduce that the output of a sample and hold circuit is defined by

Where h(t) is an impulse response representing the action of the sample and hold circuit.

Correspondingly the spectrum of the output of the sample and hold circuit is given by

Where G(f) is the fourier transform of the original analog signal g(t) and H(f) is the transfer function of the sample and hold circuit as shown byH(f)=Tssinc(fTs)exp(-jπfTs)In order to recover the original signal g(t) without distortion,we need to pass the output of the sample and hold circuit through a low pass filter designed to remove components of the


24


spectrum U(f) at multiples of the sampling rate fs and an equalizer whose amplitude response equals 1/|H(f)|.The operations are illustrated in the figure given below.

Signal Reconstruction:5.Prove that the reconstructed signal has minimum Mean square error, if it obeys sampling theorem. (page no:201-204)

(16)OR

Prove that a stationary message process contains no frequencies higher than W hertz, can be reconstructed from its samples at a sequence of points spaced ½ W seconds apart with zero mean squared error.

ORExplain the reconstruction of a message process from its samples.

When a side sense stationary message process is reconstructed from the sequence of its samples taken at a rate equal to twice the highest frequency component, the reconstructed process equals the original process in the mean-square sense for all time.

Consider then wide sense stationary message process X(t) with autocorrelation function Rx(τ) and power spectral density Sx(f).We assume that

Sx(f)=0 for |f|≥WBased on the infinite sequence of samples the reconstructed process can be denoted using X’(t)

Where X(n/2W) is the random variable obtained by sampling or observing the message process X(t) at time t=n/2W.The mean square value of the error between the original message process X(t) and the reconstructed message process X’(t) equals


25

Analog Waveform

EqualizerLow-Pass Filter

Sample and Hold

Circuit

Sampled Waveform


For a stationary process the expectation E[X(t)X’(t)] is independent of time t. Hence

Representing Rx(τ) in terms of the samples taken at τ=n/2W as

Thus we can state the sampling theorem for message processes as “If the stationary message process contains no frequencies higher than W hertz,it may be reconstructed from its samples at a sequence of points spaced 1/2W seconds apart with zero means squared error(i.e.zero power)

Quantization- Uniform & non-uniform quantization:

6.Discuss in detail about the two types of quantization. M’11, N/D’13 (16)(page no:193-195)

Quantization: The conversion of analog signal value into digital signal value. The analog value is assigned to the nearest digital value.Types of Quantization:

1. Uniform quantization and 2. Non uniform quantizationUniform quantization - When the quantization levels are uniformly distributed over the full range, the quantiser is called a uniform quantiser.

Quantile interval:The quantized levels may assume positive and negative values. The step size between quantization levels, called quantile interval, is denoted by q volts.

Types of uniform quantization.


26


Midtread quantizer – Mid-tread quantizers do have a zero output level, and can reach arbitrarily low bit rates per sample for input distributions that are symmetric and taper off at higher magnitudes.

Midriser quantiser – Mid-riser uniform quantizers do not have a zero output value their minimum output magnitude is half the step size. It also always produces an output entropy of at least 1 bit per sample.

Biased quantiser – midriser and midtread quantizers are rounding quantizers. But biased quantizer is truncation quantizer.

Non uniform quantization - Quantization noise depends upon step size. In non uniform quantization the step size is not fixed. It varies according to certain law or as per input signal amplitude.

Crest factor: Crest factor describes how strong the signal peak value is with respect to its rms value.

Crest factor = peak value / rms valueCompanding: The compression of signal at transmitter and expansion at receiver is called as companding. At the receiver the signal is expanded exactly opposite to compression curve at transmitter to get original signal.

Quantization Noise:1. (a)Explain quantization noise and Signal to Noise Ratio. (8)

Quantization noise is produced in the transmitter end of a PCM system by rounding off sample values of an analog baseband signal to the nearest permissible representation levels of the quantizer.

Quantization noise differs from channel noise in that it is signal dependent. Consider a memory less quandizer that is both uniform and symmetric with a total of L

representation levels. Let x denote the quandizer input and y denote the quantizer output, then

Y=Q(x), a staircase functionSuppose the input x lies inside the interval

Jk= {xk<x≤xk+1} k=1,2,……LWhere xk and xk+1 are decision thresholds of the interval Jk The probability density function of the quantization error is given as FQ(q),

FQ ( q)=¿ {1Δ

− Δ2≤q≤ Δ

2¿¿¿¿

The mean of the quantization error is zero and its variance σ2Q=E [Q2]

σ2Q=1Δ

∫−Δ/2

Δ/2

q2dq

=Δ2

12The output signal to quantization noise ratio (SNR) as


27

http://en.wikipedia.org/wiki/Entropy_(information_theory)


(SNR )0=σ2 x

σ2Q= σ 2 xΔ2 /12

The smaller we make the steps size the larger will the SNR.

7. (b) Derive the expression for the signal to distortion Ratio (SDR) for a given message process X (t) with power spectral density Sx(f). (8)(page no:492-493)

Consider then a message process X (t) that is wide-sense stationary but not strictly band limited. Specifically for sampling rate fs, we have

Sx(f)≠0 |f|>fs/2Where Sx(f) is the power spectral density of the process.

H l( f )=¿ {1 |f |<W ¿ ¿¿¿Let Xi(t) denote the random process resulting at the low-pass filter output, which is strictly band limited to fs/2,that is

Sxl( f )=¿ {Sx ( f ) |f |< f s /2¿ ¿¿¿The second filter has the transfer function

Hh ( f )=¿ {0 |f| < f s /2¿ ¿¿¿The mean squared error can be expressed as

ξ= ∫|f |> f s/2

Sx( f )df

The total power (mean-square value) of the process X(t) is given by

P=∫−∞

∞

Sx( f )df

Hence we can define the signal to Distortion Ratio (SDR) as

SDR=Pξ

=∫−∞

∞

S x( f )df

∫|f |> f s /2

Sx( f )df

Thus given a message process X (t) with power spectral density Sx(f).

8. Write a note on spectral Waveform Encoding. A/M’11, N/D’11, N/D’13 (16) (OR)

Explain in detail about a) Sub Band Coding b) Adaptive Transform Coding. N/D’12(page no:211-215)


28


Spectral Waveform Encoding: The spectral waveform coding, coding is done by decomposing the signal in various frequency sub Bands and separately encoding the signal in each sub band. Sub Band Coding: The sub band coding is used for speech and image signals, here in the coding the signals is divided into a small number of sub Bands and the time waveform in each sub band is encoded separately. QMF: Quadrature mirror filter (QMF), it can deliver an alias-free response due to its perfect reconstruction property. By using QMFs in subband coding, the lower frequency band is repeatedly subdivided into factors of two and then the output is decimated by a factor of two to reduce the sampling rate by half. Wavelet processing: QMF filters are implemented as digital filters and now the technique is called wavelet processing. With processing, much flexibility can be achieved for decomposing the signal as well as encoding it.Adaptive Transform Coding: Adaptive transform coding, is the technique where the signal is sampled and subdivided into frames of samples. The data in each frame is transformed into the spectral domain (i.e., frequency domain) for encoding and this is transmitted.KL transform: it is optimal in that it yields spectral values that are uncorrelated, but KLT is generally difficult to compute. Merits:

Encoded data rate is reduced. Effects of noise are reduced. Adaptive coding techniques can be employed

Demerits: The complexity of system is increased. QMFs are not ideal filters. Hence overlapping sub bands is possible.

9. Compare the performances of various speech encoding methods. M/J’13(16)Performance comparison of encoding methods: (page no:216-218)

Encoding mtd. quantizer Coder (bits) Transmission rate(Kbps)

PCM Linear 12 96CM Logarithmic 7-8 56-64DPCM Logarithmic 4-6 32-48ADPCM Adaptive 3-4 24-32DM Binary 1 32-64ADM Adaptive Binary 1 2.4-4.8

PCM: If a PAM signal is first quantized and then converted to a digital code, we get a complete digital signal. This signal is called pulse coded modulated signal and the process is known as pulse coded modulation (PCM). DPCM: The redundancy if it is reduced, then overall bit rate will decreases and number of bits required to transmit one sample will also be reduced. This type of digital pulse modulation scheme is called differential pulse coded modulation.ADPCM: Adaptive differential pulse-code modulation (ADPCM) is a variant of differential pulse-code modulation (DPCM) that varies the size of the quantization step, to allow further reduction of the required bandwidth for a given signal-to-noise ratio.


29

http://en.wikipedia.org/wiki/Signal-to-noise_ratio

http://en.wikipedia.org/wiki/Differential_pulse-code_modulation

http://en.wikipedia.org/wiki/Differential_pulse-code_modulation


Delta modulation: The high sample to sample correlation of speech type signals is exploited to the maximum in delta modulation.ADM: In the steep segment of the signal x(t), the step size is increased. When the input is varying slowly, the step size is reduced. Then the method is called as adaptive delta modulation (ADM).

LPC: In this scheme the basic assumption is that it is always possible to simulate the sampled speech sequence x[n], n=0,1,….n-1 by applying an appropriate excitation sequence v[n] to a discrete time linear filter with an all-pole transfer function H(z), representing the human vocal tract.

PCM:10. Explain a PCM system. Derive the expression for quantization noise of a PCM system

with uniform quantiser. M/J’12, M/J’13 (16)PCM: If a PAM signal is first quantized and then converted to a digital code, we get a complete digital signal. This signal is called pulse coded modulated signal and the process is known as pulse coded modulation (PCM). Block diagram:

TRANSMITTER

RECEIVERCv

PCM word size: For digital telephone channels, each speech sample is PCM encoded using 8 bits, yielding 28 or 256 level per sample.

l > log2 (1/2p) bitsPCM bandwidth: PCM signal is quantized and encoded PAM signal. The bandwidth of any digital signal depends on both symbol rate and pulse shape. The least transmission bandwidth of PCM system in terms of signal bandwidth is

BT PCM > lBRegenerative repeaters: A link usually runs for several hundred kilometers and to overcome signal losses over such a long path, the signal is boosted at intermediate stations called repeaters. Each repeater consist of both transmitter and receiver block. So baseband signal power requirement is 9.27dB less for a regenerative repeaterNoise in a PCM system:

aliasing noise.-.Due to improper sampling quantization noise.-.Occurs in transmitter itself Channel noise.-.Occurs outside the transmitter and cannot follow any deterministic

pattern. Inter symbol interference - due to high data transmission rate.

Aliasing noise comes due to improper sampling.quandisation noise occurs in the transmitter itself. Its value is completely known from the specifications of the quantiser, it can be easily tackled.


30

SAMPLER QUANTISER ENCODER

QUANTISER DECODER HOLDING CIRCUIT LPF


The next cause of degradation is the channel noise which occurs outside the transmitter and cannot follow any deterministic pattern.so it should be modeled with the help of statistical considerations.

The last cause of degradation is not noise but an interference called inter symbol interference.

In PCM where all these degradations are present, we have to analyze each degradation separately. Hence we have to derive the ratio of signal to noise power of a PCM when only quantization noise is present.

In such cases the reconstructed signal at the receiver is given as

The probability of error for a PCM system is given as

The average SNR for a PCM signal Received by the receiver is

Advantages: High noise immunity, used for storage systems (CD recording, hard disk recording), used for baseband transmission of the signal.

TDM:10.Explain about the time division multiplexing with neat diagram. (16)

(page no:227-229)

An important feature of pulse amplitude modulation is a conservation of time. So for a given message signal, transmission of the associated PAM wave engages the communication channel for only a fraction of the sampling interval on a periodic basis.

Hence some of the time interval between adjacent pulse of the PAM wave is cleared for use by other independent message signals on time shared basis.

This system is known as the time division multiplexing, which enables the joint utilization of a common channel by a plurality of independent message signals without mutual interference.

The concept of TDM is, each input message signal is first restricted in bandwidth by a low pass pre-alias filter to remove the frequencies that are non-essential to an adequate signal representation.

The pre-alias filter outputs are then applied to a commutator, which is usually, implemented using electronic switching circuitry. The function of the commutator is two-fold,

To take a narrow sample of each of the N input messages at a rate fs, that is slightly higher than 2W, where W is the cut off frequency of the pre-alias fliter.

To sequentially interleave these N samples inside a sampling interval Ts=1/fs. This function is the essence of the time division multiplexing operation. In the communication process the multiplexed signal is applied to a pulse amplitude

modulation the purpose of which is to transform the multiplexed signal into a form suitable for the transmission over the communication channel.

The N message signals to be multiplexed have similar spectral properties. Then the sampling rate for each message signal is determined in accordance with the sampling theorem.


31


Let Ts denote the sampling period so determined for each message signal. Let Tx denote the time spacing between adjacent samples in the time multiplexed signal.

It is rather obvious that Tx=Ts/N


32

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