CS Lec4,5 11feb

EE334: Communication SystemsBE-VI

LECTURE 4LECTURE 4

11th Feb,2014

review

Signals

Complex Waves and HarmonicsSine Wave

Square Wave

Saw tooth Wave

Conversion/Signal Formatting

Character Coding

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Formatting

• Character coding

• Sampling

• Quantization

• Pulse Code Modulation(PCM)• Pulse Code Modulation(PCM)

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Formatting and Transmission of

baseband signal

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Input Signal

1. Textual

2. Digital

3. Analog

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Different Conversion Scheme

1. Digital to Digital conversion

• done

2. Analog to Digital Conversion (Codec)

First Step: Pulse Amplitude Modulation (PAM)

• According to Nyquist theorem, the sampling rate must be at least two times the frequency to ensure the accurate reproduction of the original signal.

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First Step: Pulse Amplitude Modulation (PAM)

Second step: Quantized PAM Signal

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Quantizing Using Sign and Magnitude

Third Step: Pulse Code Modulation

(PCM)

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Out of each sample, Telephone companies only uses the upper 7 bits. The lower bit (bit 0) is always assumed to be 0. For example, sampling values:

+024 � +024, +038 � +038,

+025 � +024, +039 � +038

This is not affecting sampling values much.

In transmission, the most significant bit is used for control purposes, as we will see later.

Remember this

From Analog to PCM digital signal

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Sample Theorem

Need for sampling:

In analog signal, distortion is produced, and it

is difficult to recover the signal, However it is

easy to do so in digital signal.easy to do so in digital signal.

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Sampling Theorem(contd.)

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Sampling(contd.)

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Impulse Sampling

Use of Impulse:

At a particular point, we get a sample.

When any function is multiplied by impulse When any function is multiplied by impulse function at t=xsec, we get a sample of that function at x sec.

If we want to recover complete signal we have to multiply by impulse train.

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Impulse sampling(contd.)

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Impulse sampling : Using convolution

property

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Natural Sampling

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Sampling Theorem using frequency

shifting property of Fourier Transform

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Under and over sampling

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Over and under sampling

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Aliasing

Aliasing refers to an effect that causes different

signals to become indistinguishable (or aliases

of one another) when sampled. It also refers to

the distortion that results when the signalthe distortion that results when the signal

reconstructed from samples is different from the

original continuous signal.

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Aliasing

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Use of Filters

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Use of Filters

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Converting bit into samples

• Quantizing

• Similar concept to pixelization.

• Breaks wave into pieces, assigns a value in a

particular rangeparticular range

• 8-bit range allows for 256 possible sample

levels

• More bits means greater detail, fewer bits

means less detail

Quantization/Digitizing/PCM

Uniform Quantization

Non uniform Quantization

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Analog to Digital Conversion

(Sampling)

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PCM

PCM

PCM

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Non-Uniform Uniform

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Non Uniform Quantization

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Companding

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Quantization Levels

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PCM

PCM uses a sampling rate of 8000 samples per

second.

Each sample is an 8 bit sample resulting in a Each sample is an 8 bit sample resulting in a

digital rate of 64,000 bps (8 x 8000).

• n=number of pulses(bit)

• L=M=number of levels=2^n

• Step size= 2A/M

• s0=m^2(t)• s0=m^2(t)

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Quantization Error

• Analog voice data must be translated into a series of binary digits before they can be transmitted.

• With Pulse Code Modulation (PCM), the amplitude of the sound wave is sampled at amplitude of the sound wave is sampled at regular intervals and translated into a binary number.

• The difference between the original analog signal and the translated digital signal is called quantizing error.

3. Digital to Analog Modulation

(Modem)

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4. Analog to analog Conversion

Amplitude Modulation

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Frequency Modulation

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Structure of Telephone System

• End office, known also as local central office

• Local loops (twisted pairs, analog signaling)

• Trunks (fiber optics or microwave, mostly digital)

• Intermediate switches

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Need for A/D and D/A conversions

• Modem converts D/A signals

• Codec converts A/D signals

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Question of Lecture

• What is the difference between time and frequency domain?

• Any complex waveform is composed of?

• A square wave is composed of?

• A saw tooth wave is composed of?

• Prove that sine wave is composed of main frequency and all • Prove that sine wave is composed of main frequency and all harmonics using Fourier series?

• Prove that square wave is composed of main frequency and all odd harmonics using Fourier series?

• Read what is ASCII coding?

• What is M-ary pulse modulation

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Asssignment#1

Due Date: 21Feb, 2014

1. Prove through Fourier series that sine waveform is a fundamental waveform?is a fundamental waveform?

2. What is the harmonic composition of a square wave?

3. Draw and explain the basic communication system taking PSTN as an exemplary network?

4. What is m-ary pulse modulation?

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