EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING 1 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING QUESTION BANK UNIT I INTRODUCTION 1. What are energy and power signals? (APR/MAY 17) Energy signal: A finite energy signal is periodic sequence, which has a finite energy but zero average power. Power signal: An Infinite energy signal with finite average power is called a power signal. 2.Describe sampling theorem. (APR/MAY 17) According to the sampling theorem, a band limited continuous time signal x(t) can be represented in its samples and can be recovered back when sampling frequency f s is greater than or equal to the twice the highest frequency component of message signal Also, the sampling rate of 2fm samples per second is called the nyquist rate and its reciprocal 1/2πfm is called nyquist period. 3. Distinguish between digital signal & discrete-signal representation.(NOV/DEC 16) Discrete signal is well known as Discrete time signal which holds a specific value at a specific time instant. It can be obtained by sampling a continuous signal. Here the sequence is formed by collecting samples at various time instants these instants may be regular or irregular. Fig: Discrete Time signal A digital signal is a signal that represents a sequence of discrete values. In digital electronics a digital signal is a train of pulses, i.e. a sequence of fixed-width square-wave Electrical pulses or light pulses, each occupying one of a discrete number of levels of amplitude.
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EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
1 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE
EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
QUESTION BANK
UNIT I INTRODUCTION
1. What are energy and power signals? (APR/MAY 17)
Energy signal: A finite energy signal is periodic sequence, which has a finite energy but zero
average power.
Power signal: An Infinite energy signal with finite average power is called a power signal.
2.Describe sampling theorem. (APR/MAY 17)
According to the sampling theorem, a band limited continuous time signal x(t) can
be represented in its samples and can be recovered back when sampling frequency fs is
greater than or equal to the twice the highest frequency component of message signal Also,
the sampling rate of 2fm samples per second is called the nyquist rate and its reciprocal
1/2πfm is called nyquist period.
3. Distinguish between digital signal & discrete-signal representation.(NOV/DEC 16)
Discrete signal is well known as Discrete time signal which holds a specific value at a
specific time instant. It can be obtained by sampling a continuous signal. Here the sequence is
formed by collecting samples at various time instants these instants may be regular or
irregular.
Fig: Discrete Time signal
A digital signal is a signal that represents a sequence of discrete values. In digital
electronics a digital signal is a train of pulses, i.e. a sequence of fixed-width square-wave
Electrical pulses or light pulses, each occupying one of a discrete number of levels of
amplitude.
EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
2 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE
Fig:Digital Signal
4.IF x(n)=x(n+1)+x(n-2),is the system causal system? (NOV/DEC 16)
ANS: The system is non causal system(present, past& future )
5.Determine the system is causal system y(n)=x(n)+1/(x(n-1)) (MAY/JUNE 16)
ANS: The system is causal system(present, past only)
6. What is anti-aliasing filter. (MAY/JUNE 16)
A filter is used to reject frequency signals before it is sampled to reduce the aliasing is anti-
aliasing filter
7. Given a continuous time signal x(t)= 2cos500πt. What is the Nyquist rate and
fundamental frequency of the signal? (NOV/DEC 15)
ω=500π.
2πf=250π.
f=250Hz.
Nyquist rate Fs=2fm= 2x250= 500Hz.
8. Determine whether x[n]=u[n] is a power signal or an energy signal.
The energy of a discrete time signal x(n) is defined as
The average power of a discrete time signal x(n) is defined as
Here E=infinite and P= Finite. Therefore the given signal is a power signal.
9. . Define static and dynamic systems
When the output of the system depends only upon the present input sample, then it is called
static system, otherwise if the system depends pa t values of input then it is called dynamic
system
10. Define stability of a DT system.
EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
3 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE
11. Mention few applications of Digital Signal processing
* Speech processing – Speech compression & decompression for voice storage system .
* Communication – Elimination of noise by filtering and echo cancellation.
* Bio-Medical – Spectrum analysis of ECG, EEG etc.
12. Write down the expressions for discrete time unit impulse and unit step functions?
Impulse signal δ(n): The impulse signal is defined as a signal having unit magnitude at n = 0
and zero for other values of n
Unit step signal u(n): The unit step signal is defined as a signal having unit magnitude
for all values of n ≥ 0 . U(n)=1 for n≥1 ,0; n<0
13. What is Discrete Time Systems?
The function of discrete time systems is to process a given input sequence to generate output
sequence. In practical discrete time systems, all signals are digital signals, and operations on
such signals also lead to digital signals. Such discrete time systems are called digital filter.
14. Write the Various classifications of Discrete-Time systems.
Linear & Non linear system
Causal & Non Causal system
Stable & Un stable system
15. Define Linear system.
A system is said to be linear system if it satisfies Super position principle. Let us consider
x1(n) & x2(n) be the two input sequences & y1(n) & y2(n) are the responses respectively,
T[ax1(n) + bx2(n)] = a y1(n) + by2(n).
16. Define Signal& System.
A signal is a function of one or more independent variables which contain some information.
Eg: Radio signal, TV signal, Telephone signal etc.
A system is a set of elements or functional block that is connected together and produces an
output in response to an input signal. Eg: An audio amplifier, attenuator, TV set etc.
17. Is the system Y(n)=ln{x(n)} linear and time invariant?
Sol: Nonlinear, Time Invariant.
18. What is quantization error? (May 2015)
Quantization also forms the core of essentially all lossy compression algorithms. The
difference between an input value and its quantized value (such as round-off error) is
referred to as quantization error.
EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
4 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE
19. What are the advantages of DSP?
Cheaper, Greater accuracy
Ease of data storage
Implementation of sophisticated algorithms.
Flexibility in configuration
Repeatability
Adaptability
Universal Compatibility
VLF Signal Applications
20. What are the basic elements used to construct the block diagram of discrete time
system?
The basic elements used to construct the block diagram of discrete time Systems are Adder,
constant multiplier &Unit delay element.
UNIT II DISCRETE TIME SYSTEM ANALYSIS
1. What are the properties of (ROC) region of convergence? (APR/MAY 17)
ROC contains strip lines parallel to jω axis in s-plane.
If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane.
If x(t) is a right sided sequence then ROC : Re{s} > σo.
If x(t) is a left sided sequence then ROC : Re{s} < σo.
If x(t) is a two sided sequence then ROC is the combination of two regions.
2.Find the convalution of the input signal {1,2,1} and its impulse is {1,1,1} using Z
transform? (APR/MAY 17)
Sol:{1,3,4,3,1}
3. Explain the relationship between laplace transform & fourier transform.
(NOV/DEC 16)
X(jΩ) = X(s) when s=jΩ This states that laplace transform is same as fourier transform when
s=jΩ.
4. What is meant by region of convergence(ROC) of Z transform?state its properties.
The region of conve X(z) is the set of all values of z for which X(z) attains a finite value.
5. State initial value theorem& final value theorem.
If x(n)and X(z) are z-Transform pairs, then the initial value of x(z) ,
provided that the first derivative of x(t) should be Laplace transformable.
If x(n)and X(z) are z-Transform pairs, then the final value of x(z) is given as
EE6403 DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING
5 | Prepared by Mr.S.SANTHOSH M.E., ASST.PROF/ECE/SJCE
have no pole on or outside the unit circle.
6. State the convolution property of fourier transform.
If x1(t) and x1(f) is fourier transform pairs and x2(t) and x2(f) are fourier transform pairs,
then F[x(t)*h(t)] = X(jω).H(jω)
7. Find the Laplace transform of the signal x(t) = e-at u(t). (Apr/May, 2010)