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Manual – Digital Signal Processing
TABLE OF CONTENTS
Sr.No. CONTENTS Page No.
1 Difference Equation 2
2 Sampling Theorem 4
3 DTFS & DTFT 6
4 DFT 8
5 DT System Response 10
6 Z – Transform 12
7 Design of IIR Filter(Impulse Invariance) 14
8 Design of IIR Filter(Bilinear transformation) 16
9 Rectangular & hamming window 18
10 Interpolation & Decimation 20
11 Overlap & add method
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Manual – Digital Signal Processing
EXPERIMENT NO : 01
TITLE OF EXPERIMENT: Difference Equation.
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Manual – Digital Signal Processing
1.1 Aim: To find total response of discrete time system described by difference equation.
1.2 Equipment / Apparatus: PC with MATLAB software.
1.3 Theory: Take two difference equation
A) y(n)-0.5y(n-1)=x(n) y(-1)=16 x(n)=n2
B) y(n)-y(n-1)+0.24y(n-2)=x(n)-2x(n-1) y(-1)=2 y(-2)=1 x(n)=n
Solve first difference equation by any method either with
A) CF+PI OR
B) Natural & forced response approach.
1.4 Lab Session Expectation:
A) Implement above two equations in MATLAB & verify the answer of first equation theoretically as well as with the output of MATLB.
B) Implement second equation & calculate answer of few indices.
1.5 Questions:
A) How many ways are available to solve difference equation?
B) What is the relation between convolution & forced response?
C) Mention the particular inputs & their respective PI answered?
1.6 Printouts Expected:
A) MATLAB code
B) Output of the code
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Manual – Digital Signal Processing
EXPERIMENT NO: 02
TITLE OF EXPERIMENT: Sampling Theorem
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Manual – Digital Signal Processing
2.1 Aim: To study sampling Theorem & Aliasing.
2.2 Equipment / Apparatus: PC with MATLAB software.
2.3 Theory : x(t)=3 cos2000πt + 5 sin 6000πt + 10 cos12000πt
A) What is Nyquist rate?B) Let Fs=5000 samples/sec. what is discrete time signal obtained?C) Solve above Numerical.
2.4 Lab session expectation:
A) Generate two sin waves (100Hz,600Hz)
B) Sample them with Fs=500Hz
C) Plot x1(n) & x2(n)
2.5 Questions:
A) How do you understand the concept of aliasing from above experimentation?
B) What exactly is the meaning of aliasing & why it happens?
C) Can aliasing be avoided?
D) Is there any application of aliasing?
E) If the analog signal is not band limited can we sample it without aliasing?
F) Why the range of digital frequencies –π to π?
G) In the above experimentation change the sampling frequency suitably &
show that aliasing can be avoided.
2.5 Printouts Expected:
A) MATLAB code.
B) Output to demonstrate aliasing.
C) Output to demonstrate aliased free condition.
2.6 Useful Functions: sin, cos, stem, subplot
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Manual – Digital Signal Processing
EXPERIMENT NO: 03
TITLE OF EXPERIMENT: DTFS & DTFT
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Manual – Digital Signal Processing
3.1 Aim: To find DTFS for periodic & non periodic signals
3.2 Equipment / Apparatus: PC with MATLAB software.
3.3 Theory :
A) Take a square wave & represent in terms of DTFS.
B) Take exponential signal & calculate its DTFT.
3.4 Lab session expectations: Part A
A) Generate a square wave(symmetric around x axis)B) Calculate DTFS coefficientsC) Generate square wave(with dc shift completely above x axis)D) Calculate DTFS coefficients
Part B
A) Generate exponential signal B) Select resolution of frequency axisC) Plot DFT of sequence
3.5 Questions:
A) What is difference between DTFS & DFT?B) Why the transform is called DTFT?C) Comment on the observations of part AD) Verify the harmonics present in square wave & justify the observation.E) Comment on the nature of DTFT & how it is different than CTFT.
3.6 Printouts:
A) MATLAB code
B) waveforms
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Manual – Digital Signal Processing
EXPERIMENT NO: 04
TITLE OF EXPERIMENT: DFT
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Manual – Digital Signal Processing
4.1 Aim : To find DFT of DT signal
4.2 Equipment / Apparatus: PC with MATLAB software.
4.3 Theory :
A) X (n) = [1, 2, 3, 4], Calculate 4 point DFT.B) Write the time shifting property of DFT & justify why we have circular shift
& not linear shift.C) Explain concept of DFT.
4.4 Lab session Expectation :
A) Take any sequence & find its DFT.B) Take a sinusoidal signal & calculate its DFT.C) Verify time shifting property of DFT for the above sequence.D) Verify results of DFT with the function FFT available in MATLAB.
4.5 Questions:
A) Justify the plot of DFT of the sine wave used.B) Can we identify the frequency present in a signal just looking at the plot of
FFT? If yes justify. If not justify.C) How many computations are required to calculate N point DFT?D) Explain the concept of convolution in the DFT sense?
4.6 Printouts:
A) DFT ProgramB) Property verification codeC) Output of above two steps.
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EXPERIMENT NO: 05
TITLE OF EXPERIMENT: DT system response
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Manual – Digital Signal Processing
5.1 Aim: To find response of DT system using convolution.
5.2 Equipment / Apparatus: PC with MATLAB software.
5.3 Theory:
A) Write equation of convolution.B) Take two sequences & calculate convolution.
5.4 Lab session Expectation:
Approach 1
A) Take nay sequences h(n),x(n)B) Compute convolution.C) Verify the result using ‘conv’ function.
Approach 2
A) Take discrete time system e.g. y(n)-3y(n-1)=x(n) x(n)=2^nB) Obtain h (n) from this equation.C) Compute y(n) with above h(n) & input x(n)
Hint: y (n) =h (n) when x (n) =δ (n)
5.5 Printouts expected:
A) MATLAB code
B) OUTPUT
5.6 Questions:
A) Why do we study basic signals?
B) What is theme of convolution?
C) What is the application of linear convolution?
D) Y (n) =x2(n) Will convolution work for such a system? Justify the answer.
E) What is the limitation of ‘conv’ function in MATLAB?
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Manual – Digital Signal Processing
EXPERIMENT NO: 06
TITLE OF EXPERIMENT: Z Transform
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Manual – Digital Signal Processing
6.1 Aim: To find inverse Z transform & to sketch pole zero plot of a given rational function.
6.2 Equipment / Apparatus: PC with MATLAB software.
6.3 Theory: A) Definition of Z Transform.
B) Unit circle importance, ROC concept.
C) Take any rational function in Z domain & calculate its inverse using
I) Partial fraction method
II) Long division method
D) Take any function & sketch its pole zero plot.
6.4 Lab session Expectation:
A) Implement the above example in MATLAB & verify the results.
B) Plot pole zero graph & frequency response.
6.5 Questions:
A) Why do we go with Z Transform?
B) Comment on stability of system from pole zero plot.
C) What is the relation between Z Transform & DTFT?