Matlab Dsp

S.U.S. WOMEN ENGINEERING COLLEGETANGORI (MOHALI)

LAB FILE

Digital Signal Processing Using Mat Lab 7.1

Submitted to: Submitted by:Er.Aarti Hina Pradip Sangai 81003108013 6th Semester Branch-ECE

Hina Pradip Sangai 81003108013

List of Experiments

1. Introduction about Mat lab.

2. To develop sine and cosine function waveforms.

3. To develop elementary signals: Unit step signal, unit ramp signal, unit impulse signal, exponential signal.

4. Develop program modules based on operation on sequences like: Signal addition, Signal multiplication, Signal folding, Signal Shifting.

5. To develop program to perform linear convolution of two input Sequence x(n) and h(n). Plot x(n) and h(n) and result of linear convolution as y(n)on single plot and verify the result mathematically.

6. To obtain the impulse response of the system described by difference equation: y(n)-0.5y(n-1)=x(n)

7. Write a program to determine and plot poles and zeroes of rational Z-transform given as:- H(z)=(5+z-1)(3+z-1 ) - ------------------

(2+z-1)(4+z-1)

8. To develop program for computing DFT and IDFT.

9. To develop program for finding magnitude and phase response of LTI system described by difference equation : y(n)=0.8y(n-2)+x(n)-x(n-2)

10. To design an IIR filter with following specifications using filter design and analysis toolbox Response type: Low pass filter

Design method: IIR Butterworth filter Filter order: Minimum Match exactly: Stop band Frequency specifications: Units=KHz Fs=500 Fpass=100 Fstop=150 Magnitude specifications: Units=dB Apass=3 Astop=1

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EXPERIMENT-1INTRODUCTION ABOUT MATLAB

MATLAB® is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include:

Math and computation Algorithm development Data acquisition Modeling, simulation and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development, including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar noninteractive language such as C or Fortran.

The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide easy access to matrix software developed by the LINPACK and EISPACK projects. Today, MATLAB engines incorporate the LAPACK and BLAS libraries, embedding the state of the art in software for matrix computation.

Desktop Overview

Use desktop tools to manage your work in MATLAB. You can also use MATLAB functions to perform the equivalent of most of the features found in the desktop tools.

The following illustration shows the default configuration of the MATLAB desktop. You can modify the setup to meet your needs.

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The MATLAB System

The MATLAB system consists of five main parts:

Desktop Tools and Dvelopment Environment. This is the set of tools and facilities that help you use MATLAB functions and files. Many of these tools are graphical user interfaces. It includes the MATLAB desktop and Command Window, a command history, an editor and debugger, and browsers for viewing help, the workspace, files, and the search path.

The MATLAB Mathematical Function Library. This is a vast collection of computational algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

The MATLAB Language. This is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create large and complex application programs.

Graphics. MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well as annotating and printing these graphs. It includes high-level functions

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for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It also includes low-level functions that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your MATLAB applications.

The MATLAB External Interfaces/API. This is a library that allows you to write C and Fortran programs that interact with MATLAB. It includes facilities for calling routines from MATLAB (dynamic linking), calling MATLAB as a computational engine, and for reading and writing MAT-files.

Programming:

Flow Control:MATLAB has several flow control constructs:

if, else, and elseif switch and case for while continue break try - catch return

Several special functions provide values of useful constants:

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Operators

Expressions use familiar arithmetic operators and precedence rules.

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EXPERIMENT-2

% Develop sine and cosine function waveforms t=linspace(0,10,100);y=sin(pi*t);plot(t,y);y2=cos(pi*t);hold onplot(t,y2,'red');xlabel('time');ylabel('amplitude');title('sine and cosine waveforms');

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WAVEFORMS:-

0 1 2 3 4 5 6 7 8 9 10-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time

ampl

itude

sine and cosine waveforms

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EXPERIMENT-3

% Develop elementary signals: 1) Unit step signal 2) unit ramp signal 3) unit impulse signal 4) exponential signal.

t=-3:1:3;y=[zeros(1,3),ones(1,4)];subplot(2,2,1);stem(t,y);xlabel('time');ylabel('amplitude');title('unit step function');t1=-4:1:4;y1=t1;subplot(2,2,2);stem(t1,y1);xlabel('time');ylabel('amplitude');title('unit ramp function');t2=-3:1:3;y2=[zeros(1,3),1,zeros(1,3)];subplot(2,2,3);stem(t2,y2);xlabel('time');ylabel('amplitude');title('unit impulse function');t3=-5:1:5;y3=exp(t3);subplot(2,2,4);stem(t3,y3);xlabel('time');ylabel('amplitude');title('exponential function');

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WAVEFORMS:-

-4 -2 0 2 40

0.5

1

time

ampl

itude

unit step function

-4 -2 0 2 4-4

-2

0

2

4

timeam

plitu

de

unit ramp function

-4 -2 0 2 40

0.5

1

time

ampl

itude

unit impulse function

-5 0 50

50

100

150

time

ampl

itude

exponential function

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EXPERIMENT-4

%Develop program modules based on operation on sequences like: 1) Signal addition 2) Signal multiplication3) Signal folding 4) Signal shifting

t=0:1:5;x=[1,2,3,4,5,6];subplot(4,3,1);stem(t,x);xlabel('time');ylabel('amplitude');title('x sequence');t1=0:1:5;y=[0,-1,1,2,3,2];subplot(4,3,2);stem(t1,y);xlabel('time');ylabel('amplitude');title('y sequence');z=x+y;subplot(4,3,3);stem(z);xlabel('time');ylabel('amplitude');title('addition of x and y sequence');t2=0:1:5;x1=[1,2,3,4,5,6];subplot(4,3,4);stem(t2,x1);xlabel('time');ylabel('amplitude');title('x sequence');t3=0:1:5;y1=[0,1,1,2,3,2];subplot(4,3,5);stem(t3,y1);xlabel('time');ylabel('amplitude');title('y sequence');z1=x.*y;subplot(4,3,6);stem(z1);xlabel('time');ylabel('amplitude');title('multiplication of x and y sequence');t4=0:1:5;x2=[1,2,3,4,5,6];subplot(4,3,7);stem(t4,x2);

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xlabel('time');ylabel('amplitude');title('x sequence');z2=-x2;subplot(4,3,8);stem(t4,z2);xlabel('time');ylabel('amplitude');title('folding of x sequence');t5=0:1:5;t5=-t4;subplot(4,3,9);stem(t5,x2);xlabel('time');ylabel('amplitude');title('folding of x sequence');t6=0:1:5;x3=[1,2,3,4,5,6];subplot(4,3,10);stem(t6,x3);xlabel('time');ylabel('amplitude');title('x sequence');t7=0:1:6;t7=t6-1;subplot(4,3,11);stem(t7,x3);xlabel('time');ylabel('amplitude');title('shifting of x sequence');t8=0:1:6;t8=t6+1;subplot(4,3,12);stem(t8,x3);xlabel('time');ylabel('amplitude');title('shifting of x sequence');

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WAVEFORMS:-

0 50

5

10

time

ampl

itude

x sequence

0 5-5

0

5

timeam

plitu

de

y sequence

0 5 100

5

10

time

ampl

itude

addition of x and y sequence

0 50

5

10

time

ampl

itude

x sequence

0 50

2

4

time

ampl

itude

y sequence

0 5 10-20

0

20

time

ampl

itude

multiplication of x and y sequence

0 50

5

10

time

ampl

itude

x sequence

0 5-10

-5

0

time

ampl

itude

folding of x sequence

-4 -2 00

5

10

time

ampl

itude

folding of x sequence

0 50

5

10

time

ampl

itude

x sequence

-5 0 50

5

10

time

ampl

itude

shifting of x sequence

0 5 100

5

10

time

ampl

itude

shifting of x sequence

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EXPERIMENT-5

%To develop program to perform linear convolution of two input sequencex(n) and h(n). Plot x(n) and h(n) and result of linear convolution as y(n)on single plot and verify the result mathematically.

t=0:1:4;x=input('enter x(n) sequence');subplot(3,1,1);stem(t,x);xlabel('time');ylabel('amplitude');title('x sequence');t1=0:1:2;h=input('enter h(n) sequence');subplot(3,1,2);stem(t1,h);xlabel('time');ylabel('amplitude');title('h sequence');t2=0:1:6;y=conv(x,h);subplot(3,1,3);stem(t2,y);xlabel('time');ylabel('amplitude');title('convolution of x and h sequence');

Result on command window :

enter x(n) sequence[1 2 3 4 5]enter h(n) sequence[ 1 2 3]

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WAVEFORMS:-

0 0.5 1 1.5 2 2.5 3 3.5 40

5

time

ampl

itude

x sequence

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

time

ampl

itude

h sequence

0 1 2 3 4 5 60

20

40

time

ampl

itude

convolution of x and h sequence

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EXPERIMENT-6

%To obtain the impulse response of the system described by differenceequation y(n)-0.5y(n-1)=x(n)

x=[ones(1,1),zeros(1,9)]a=input('enter the coeff. of y(n)')b=input('enter the coeff. of x(n)')h=filter(b,a,x)n=0:9stem(n,h)title('impulse response of the system')xlabel('n')ylabel('h(n)')

Result on command window:-

enter the coeff. of y(n)[1 -0.5]

a =

1.0000 -0.5000

enter the coeff. of x(n)[1]

b =

1

h =

1.0000 0.5000 0.2500 0.1250 0.0625 0.0313 0.0156 0.0078 0.0039 0.0020

n =

0 1 2 3 4 5 6 7 8 9

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WAVEFORMS:-

0 1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1impulse response of the system

n

h(n)

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EXPERIMENT-7

%Write a program to determine and plot poles and zeroes of rational z-transform given as H(z)= 15 z2 + 8 z + 1 H(z)=(5+z-1)(3+z-1)

--------------- or ----------- 8 z2 + 6 z + 1 (2+z-1)(4+z-1)

a=input('enter the coefficients of num.')b=input('enter the coefficients of den.')c=tf(a,b,1)[z p]=tf2zp(a,b)zplane(z,p)[r,p,k]=residuez(a,b)[num,den]=residuez(r,p,k)

Result on command window:-

enter the coefficients of num.[15 8 1]

a =

15 8 1

enter the coefficients of den.[8 6 1]

b =

8 6 1 1

Transfer function:15 z^2 + 8 z + 1----------------8 z^2 + 6 z + 1 Sampling time: 1

z =

-0.3333 -0.2000

p =

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-0.5000 -0.2500

r =

0.7500 0.1250

p =

-0.5000 -0.2500

k =

1

num =

1.8750 1.0000 0.1250

den =

1.0000 0.7500 0.1250

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POLE-ZERO PLOT:-

-1 -0.5 0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Real Part

Imag

inar

y P

art

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EXPERIMENT-8

%To develop program for computing DFT and IDFT clc;x=input('ENTER A SEQUENCE TO FIND DFT');N=8;X=fft(x,N);a=ifft(X);

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Result on the command window:-

ENTER A SEQUENSE TO FIND DFT[1 2 3 4 5]

N =

8

X =

Columns 1 through 6

15.0000 -5.4142 - 7.2426i 3.0000 + 2.0000i -2.5858 - 1.2426i 3.0000 -2.5858 + 1.2426i

Columns 7 through 8

3.0000 - 2.0000i -5.4142 + 7.2426i

a =

1.0000 2.0000 3.0000 4.0000 5.0000 -0.0000 0 -0.0000

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EXPERIMENT-9

% To develop program for finding magnitude and phase response of LTI system described by difference equation y(n)=0.8y(n-2)+x(n)-x(n-2)

clc;b=input('enter the coeff. of x(n)');a=input('enter the coeff. of y(n)');N=200;[H,W]=freqz(b,a,N);subplot(2,1,1);absH=abs(H);angH=angle(H);plot(W,absH);xlabel('W');ylabel('abs H');title('LTI magnitude');subplot(2,1,2);plot(W,angH);xlabel('W');ylabel('angle H');title('LTI angle');

Result on command window:

enter the coeff. of x(n)[1 0 -1]enter the coeff. of y(n)[1 0 -0.81]

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WAVEFORMS:-

0 0.5 1 1.5 2 2.5 3 3.50

0.5

1

1.5

W

abs

H

LTI magnitude

0 0.5 1 1.5 2 2.5 3 3.5-2

-1

0

1

2

W

angl

e H

LTI angle

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EXPERIMENT-10

% To design an IIR filter with following specifications using filter design and analysis toolboxResponse type: Low pass filterDesign method: IIR Butterworth filterFilter order: MinimumMatch exactly: Stop bandFrequency specifications:Units=KHzFs=500Fpass=100Fstop=150Magnitude specifications:Units=dBApass=3Astop=16

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Current Filter Information:

Magnitude Resoponse:

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Phase Response:

Impulse Response:

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Step Response:

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Generated MATLAB Code:-

%EXP10 Returns a discrete-time filter object. %% M-File generated by MATLAB(R) 7.1 and the Signal Processing Toolbox 6.4.%% Generated on: 23-Apr-2009 13:55:23% % Butterworth Lowpass filter designed using FDESIGN.LOWPASS. % All frequency values are in kHz.Fs = 500; % Sampling Frequency Fpass = 100; % Passband FrequencyFstop = 150; % Stopband FrequencyApass = 3; % Passband Ripple (dB)Astop = 16; % Stopband Attenuation (dB)match = 'stopband'; % Band to match exactly % Construct an FDESIGN object and call its BUTTER method.h = fdesign.lowpass(Fpass, Fstop, Apass, Astop);Hd = butter(h, 'MatchExactly', match); % [EOF]

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