sp lab report

8/3/2019 Sp Lab Report

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A

LAB REPORT

ON

SIGNAL PROCESSING

Submitted as a requirement for the partial fulfillment of

Bachelors Degree From

Rajasthan Technical University, Kota

SUBMITTED BY

SURYA PRAKASH

Final year ECE

M.L.V.Textile and engineering College.

( An Autonomous Engineering College of Govt. Of Rajasthan)

Bhilwara, Rajasthan


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ACKNOWLEDGMENT

First and foremost, we would like to express my sincere gratitude to our lab in

charge Mrs. Sarita Chauhan . We were privileged to experience a sustained

enthusiastic and involved interest from her side. This fueled our enthusiasm even

further and encouraged us to boldly step into what was a totally dark and

unexplored expanse before us. We also like to thank the MLVTEC staff members

and the institute, in general, for extending a helping hand at every juncture of need.

Keerti vyas

Yogesh kumar


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INDEX

Object Page no.

1. Introduction to MATLAB..5

2. Explain following with example....6

3. Explain commands with example.9

4. Write a program (WAP) for adding five numbers at run time.14

5. WAP checking whether a number is prime or not

(i) Using function.15

(ii) Without using function...15

6. WAP to find a number is divisible by 2 or 3 or both...16

7. WAP to find factorial of a given number.17

8. WAP to perform convolution...18

9. WAP to plot sine and cosine functions

(i) On same Window.19

(ii) On different Window..20

10. WAP to add two sine functions..21

11. WAP to perform folding of a sequence..22

12. WAP to plot Gaussian curve...23

13. WAP to plot Rayleigh probability curve24

14. WAP to design bode plot25

15. WAP to perform auto correlation and cross correlation26

16. WAP to compare the order of butterworth filter..28


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17. WAP to compare the 4th

order butterworth filter for frequency

w=100 and w=200...29

18. WAP to plot the following function on different window...........................33

a) Unit step

b) Ramp function

c) Unit impulse

19. WAP to plot the following function on same window36

a) Unit step

b) Ramp function

c) Unit impulse

20. WAP to generate the impulse sequence at no. sample laying between

n1


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EXPERIMENT NO 1

Object- Write the introduction to MATLAB.

Theory:

MATLAB is a powerful computing system for handling scientific and engineering calculations.The name MATLAB stands for Matrix Laboratory, because the system was designed to make

matrix computations particularly easy. It intended to provide easy access to the matrix libraries

developed by Linpack and Eispack projects. These are carefully tested high quality programming

packages for solving linear equations and eigen value problems.

OR,

MATLAB

is a high-level technical computing language and interactive environment for

algorithm development, data visualization, data analysis, and numerical computation. Using

MATLAB, you can solve technical computing problems faster than with traditional programming

languages, such as C, C++, and Fortran.

You can use MATLAB in a wide range of applications, including signal and image processing,

communications, control design, test and measurement, financial modeling and analysis, and

computational biology. Add-on toolboxes (collections of special-purpose MATLAB functions)

extend the MATLAB environment to solve particular classes of problems in these application

areas.

MATLAB provides a number of features for documenting and sharing your work. You can

integrate your MATLAB code with other languages and applications, and distribute your

MATLAB algorithms and applications.

MATLAB is originally written in FORTRAN developed by Cleve Moler, the chairman of computer

science department at the university of new mexico, started developing MATLAB in 1970s.

Key Features

y High-level language for technical computing

y Development environment for managing code, files, and data

y Interactive tools for iterative exploration, design, and problem solving

y Mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, andnumerical integration

y 2-D and 3-D graphics functions for visualizing data

y Tools for building custom graphical user interfaces

y Functions for integrating MATLAB based algorithms with external applications and languages,

such as C, C++, Fortran, Java, COM, and MicrosoftExcel.


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EXPERIMENT NO 2

Object- Explain the following with suitable examples.

(i) For loop

(ii) If-else

(iii) Switch case

Theory :

(i) For Loop :

for loops are often used when a sequence of operations is to be performed a predetermined

number of times. For example computing the average of a list of numbers requires adding up a

known number of values.Syntax

Loop counter incremented by one:

for i = start value : end valuex = ...y = ......end

i is the loop counter. On the first pass through the loop, i is set to start value. On the second

pass through the loop i is set to start Value+1. The Matlab statements between the for and the

end are evaluated until i>end value.

Example:Compute the sum of the _rst n integers

n = 10;s = 0;for i=1:ns = s + i;end

(ii) If-else :

Syntax :

ifexpression

statementselseifexpression

statements

else

statements

end


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Description :

ifexpression, statements, end evaluates an expression, and executes a group of statements

when the expression is true.

Else-if and else are optional, and execute statements only when previous expressions in

the if block are false. An if block can include multiple else-if statements.

An evaluated expression is true when the result is nonempty and contains all nonzero elements

(logical or real numeric). Otherwise, the expression is false.

Expressions can include relational operators (such as < or ==) and logical operators (such

as &&, ||, or ~). MATLAB evaluates compound expressions from left to right, adhering

to operator precedence rules.

Examples :

x=-5:0.1:5for i=1:101

if x(i)>=0y(i)=1else

y(i)=0end

endstem(x,y)

(iii) Switch case:

Syntax

switch switch_expression

case case_expressionstatements

case case_expression

statements

:

otherwise

statements

end

Description

A switch block conditionally executes one set of statements from several choices. Each choice isa case.

An evaluated switch_expression is a scalar or string. An evaluated case_expression is a scalar, a

string, or a cell array of scalars or strings. The switch block tests each case until one of the cases

is true. A case is true when:

For numbers, eq(case_expression,switch_expression).

For strings, strcmp(case_expression,switch_expression).

For objects that support the eq function, eq(case_expression,switch_expression).


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EXPERIMENT NO 3

Object- Explain the following commands with example.

a) whos e) zeros

b) sum f) ones

c) diag g) eyes

d) magic h) randn

a) whos : whos lists current variable, long form. It lists all the variables in the current

workspace , together with information about their size, shape, bytes, class.

Example:

b) sum :

y B= sum(A) returns sum along different dimensions of array. If a is floating point,

that is double or single.

y If A is a vector, sum(A) returns the sum of elements.

y If a is a matrix, sum(A) treats the column of A as vectors, returning a row vector

of the sum of each column.


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Example :

C)Diag:

Syntax :

x=diag(v,k)

x=diag(v)

Description : x=diag(v,k) where v is the vector of n components, returns a square matrix x of

order n+abs(k), k=0 represents the main diagonal, k>0 above the main diagonal, and k


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Example :

c) Magic:

Syntax: m=magic(n)

Description: m=magic(n) returns an nxn matrix constructed from the integers 1 through n2

with equal row and column sums. The order n must be a scalar

Example:


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d) Zeros :

Syntax : zeros(n) or zeros (m,n)

Description :

y It defines a matrix of order with all entries zero.

y

An error message will appear if n is not a scalar.

Example :

e) Ones :

Syntax : ones(n) or ones(m,n)

Description: it will generate a matrix with all entries o1. Where n must be a scalar.

Example:

f) Eyes:

Syntax : eye(n)

Description :

y It will generate a identity matrix of order nxn.

y The argument n must be scalar and it represents the order of square matrix.


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Example:

g) randn :

Syntax : randn(n) or randn(m,n)

Description :

y Normally distributed pseudorandom numbers.

y A=randn(n), returns a matrix containing pseudorandom values drawn from the

standard normal distribution.

Example :


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EXPERIMENT NO 4

Object- Write a program for addition of five numbers at run time.

Program :

sum=0;for i=1:5

u=input('enter ur number');sum=sum+u ;

enddisp('sum of number =');disp(sum);

Output:


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EXPERIMENT NO 5

Object- Write a program for checking whether a number is prime or not with and without using

function isprime.

Program :

(i) Using function isprime

u=input(Enter your number);x=isprime(u);if x==1

disp(number is prime);else

disp(number is not prime);

(ii) Without using isprime

v=0;s=1;u=input('enter ur num');for i=2:u-1

s=rem(u,i);if s==0

disp('Number is not prime');break;

endendif s~=0

v=1;disp('no is prime');

end

Output :


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EXPERIMENT NO 6

Object- Write a program to find the number divisible by 2 or 3 or both.

Program :

u=input('enter ur num');a=rem(u,2);if a==0

disp('num is divisible by 2');endb=rem(u,3);if b==0

disp('num is divisible by 3');endc=rem(u,6);if c==0

disp('num is div

isible by both 2 and 3');end

Output:


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EXPERIMENT NO 7

Object- Write a program to find factorial of a given number.

Program :

u=input('Enter your number');s=1;for i=1:u

s=s*i;enddisp('factorial of a given number is');disp(s);

Output :


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EXPERIMENT NO 8

Object- Write a program to perform convolution.

Program :

u=input('Enter first sequence');h=input('Enter second sequence');subplot(3,1,1);stem(u);title('First input sequence');subplot(3,1,2);stem(h);title('Second input sequence');

subplot(3,1,3);y=conv(u,h);stem(y)title('convolution sequence');

Output :


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EXPERIMENT NO 9

Object- Write a program to plot sine and cosine function on same and different window.

Program :

(i) On same window

x=0:0.01:4*pi;y=sin(x);z=cos(x);subplot(2,1,1);plot(y);xlabel('x-axis');ylabel('y-axis');

title('sine Function');subplot(2,1,2)plot(z);xlabel('x-axis');ylabel('y-axis');

Output :


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(ii) On differentWindow

x=0:0.01:4*pi;y=sin(x);z=cos(x);figure(1)plot(y);xlabel('x-axis');ylabel('y-axis');title('sine Function');figure(2)plot(z);xlabel('x-axis');title('cosine Function');ylabel('y-axis');

Output :


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EXPERIMENT NO 10

Object- Write a program for addition of two sine functions.

Program :

t1=0:.01:2*pi;t2=0:.01:2*pi;y=sin(t1);z=sin(t2);u=y+z;subplot(3,1,1);plot(y);title('First Sine function');subplot(3,1,2);plot(z);title('second Sine function');

subplot(3,1,3);plot(u);title('Addition');

Output:


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EXPERIMENT NO 11

Object- Write a program for folding of original sequence.

Program :

x=input('enter original sequence=');y=fliplr(x);subplot(2,1,1);stem(x);xlabel('x-axis');ylabel('amplitude');title('Original sequence');subplot(2,1,2);stem(y);xlabel('x-axis');ylabel('amplitude');

title('Folded sequence');

Input: [1 23456]

Output:


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EXPERIMENT NO 12

Object- Write a program to plot Guassian Curve.

Program :

x=0:0.1:10;y=gaussmf(x,[2,5]);plot(x,y);title('guassian curve');

Output :


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EXPERIMENT NO 13

Object- Write a program to plot Rayleigh Probability Curve.

Program :

x=0:.1:3;p=raylpdf(x,1);plot(x,p);title('rayleigh probability curve');

OUTPUT :


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EXPERIMENT NO 14

Object- Write a program to design Bode plot for a function.

Program :

g=(s^2+0.1*s+7.5)/((s^4)+0.12*s^3+9*s^2);h=tf([1 0.1 7.5],[1 0.12 9 0 0]);bode(h);grid on;

OUTPUT :


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EXPERIMENT NO 15

Object- Write a program auto-correlation and cross correlation.

Program :

Auto-correlation

x=input('enter the sequence=');y=xcorr(x,x);figure(1);subplot(2,1,1);stem(x);xlabel('x-axis');ylabel('amplitude');

title('input');subplot(2,1,2);stem(fliplr(y));xlabel('x-axis');ylabel('amplitude');title('Output');disp('the resultant signal is');

Input : [1 234]

Output:


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(2)Cross-Correlation

x=input('enter the first sequence=');h=input('enter the second sequence=');

y=xcorr(x,h);figure(1);subplot(3,1,1);stem(x);title('first Input');xlabel('n-->');ylabel('amplitude');subplot(3,1,2);stem(h);xlabel('n-->');ylabel('amplitude');title('Second Input');subplot(3,1,3);stem(fliplr(y));xlabel('n-->');ylabel('amplitude');title('Output');disp('the resultant signal is');

Given Inputs: [1 234] and [423 1]

Output:


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EXPERIMENT NO 16

Object- Write a program to compare the order of butterworth filter.

Program :

s=tf('s');w=100;g=((w^5)/((s+w)*((s*s)+(0.765*w*s)+(w*w))*((s*s)+(1.85*s*w)+(w*w))));bode(g);grid on;title('Fifth Order Butterworth Filter');h=((w^4)/(((s*s)+(0.765*w*s)+(w*w))*((s*s)+(1.85*s*w)+(w*w))));figure(2);bode(h);grid on;title('Fourth Order Butterworth Filter');

k=((w^3)/((s+w)*((s*s)+(w*s)+(w*w))));figure(3);bode(k);grid on;title('Third Order Butterworth Filter');u=((w^2)/(((s*s)+(sqrt(2)*w*s)+(w*w))));figure(4);bode(u);grid on;title('Second Order Butterworth Filter');


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Experiment No- 17Object - To compare the 4th order butterworth filter for frequency w=100 and w=200.

Program :

s=tf('s');w=100;h=((w^4)/((s*s)+(0.765*w*s)+(w*w)*((s*s)+(1.85*s*w)+(w*w))));figure(1);bode(h);grid on;title('fourth order butterworth filter for w=100');W=200;g=((w^4)/((s*s)+(0.765*w*s)+(w*w)*((s*s)+(1.85*s*w)+(w*w))));figure(2);bode(g);

grid on;title('fourth order butterworth filter for w= 200');

output:


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EXPERIMENT NO 18

Object-Write a program to plot the following function on different window.

d) Unit step b) Ramp function c) Unit impulse

Program :

a) Unit step

x=-5:0.1:5for i=1:101


y(i)=0end

endstem(x,y)xlabel('x-axis')ylabel('y-axis')

axis([-5,5,-5,5])title('Unit step response')

Output:


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b) Ramp Function

x=-5:0.1:5for i=1:101

if x(i)>=0

y(i)=

x(i)else

y(i)=0end


axis([-5,5,-5,5])title('Comtinuous Ramp signal')

Output:


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c) Unit Impulse

x=-5:0.1:5for i=1:101

if x(i)==0

y(i)=1;else

y(i)=0;end


axis([-5,5,-5,5])title('unit Impulse response')

Output:


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EXPERIMENT NO 19

Object- Write a program to plot the following function on same window.

a) Unit step b) Ramp function c) Unit impulse

Program :

x=-5:0.1:5for i=1:101


y(i)=0end

endsubplot(2,2,1)

plot(x,y)xlabel('x-axis')ylabel('y-axis')

axis([-5,5,-5,5])title('Unit step response')for i=1:101

if x(i)>=0y(i)=x(i)else

y(i)=0end

end

subplot(2,2,2)plot(x,y)

xlabel('x-axis')ylabel('y-axis')

axis([-5,5,-5,5])title('Comtinuous Ramp signal')for i=1:101

if x(i)==0y(i)=1;

elsey(i)=0;

endendsubplot(2,2,3)plot(x,y)xlabel('x-axis')ylabel('y-axis')

axis([-5,5,-5,5])title('unit Impulse response')


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EXPERIMENT-20

Object-write a program to generate the impulse sequence at no. sample layingbetween n1


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EXPERIMENT NO 21

Object- Draw a signal and apply following properties on it

b) Shifting b) Scaling c) Inverse

Program :

x=1:0.01:4*pi;y=sin(x);figure(1);plot(y);title('Original sequence')p=x-2;

z=sin(p);figure(2);plot(z);title('Shifted sequence')q=2*x;y=sin(q);figure(3);plot(y);title('Scaling');p=-x;z=sin(p);figure(4);plot(z);

title('inverse');

Output:


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Experiment No- 22

Object: write a program to perform

X= an

* u*(n)

Program:

ns=input('enter the strating point of the sequence=');ne=input('enter the ending point of the sequence=')'a=input('the value of a=');n=[ns:ne];u=[(n-ns)>=0];subplot(2,2,1);stem(n,u);title('unit signal u(n)');xlabel('Samples n');ylabel('u(n)');e=a*exp(n);

subplot(2,2,2);stem(n,e);title('exponential signal e=(a^n)');xlabel('Samples n')ylabel('e=(a^n)');m=u.*e;subplot(2,2,3);stem(n,m);title('multiplied signal m=u*e');xlabel('Samples n');ylabel('m=a*exp(n).*u');

output:


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EXPERIMENT -23

Object : write a program to generate complex exponential function

X = exp (complex(sigma,w)*n) ; sigma=0.3,w= 0.2

Program:

sigma=input('enter the value of sigma=');w=input('enter the value of w=');n=[1:100];x=exp(complex(sigma,w)*n);stem(n,x);title('generating the exponential sequence for sigma and omega');xlabel('samples n');ylabel('amplitude of x(n)');pause;

clc;clear all;close all;

output:


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EXPERIMENT-24

Object: write a program to design finite impulse response filter (low pass) for fc=0.6 & N=20.

Program:

fc=0.6;N=20;hf=fdesign.lowpass('N,fc',N,fc);hd(1)=design(hf,'window','window',@hamming);hd(2)=design(hf,'window','window',{@chebwin,50});hfvt=fvtool(hd);legend(hfvt,'hamming window design','dolph chebyshev window design');

output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

Normalized Frequency (vT rad/sample)

M

agnitu

de

(dB)

Magnitude Response (dB)

hamming window des ign

do lph chebyshev w indow des ign


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EXPERIMENT-25

Object: write a program to design kaiser window design

Fp=0.6, fst=0.7725, Ap=0.01, Ast=90

Program:

fc=0.6;n=20;hf=fdesign.lowpass('n,fc',n,fc);fp=0.6;fst=0.7725;ap=0.01;ast=90;setspecs(hf,'fp,fst,ap,ast',fp,fst,ap,ast);hd(4)=design(hf,'kaiserwin');hfvt=fvtool(hd(4));

output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-100

-8 0

-6 0

-4 0

-2 0

0


M

agnitude(d

B)



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EXPERIMENT-26

Object: write a program to perform equiripple technique to optimize Kaiser window solution.

Program:

fc=0.6;N=20;hf=fdesign.lowpass('N,fc',N,fc);fp=0.6;fst=0.7725;ap=0.01;ast=90;setspecs(hf,'fp,fst,ap,ast',fp,fst,ap,ast);hd(4)=design(hf,'kaiserwin');

hfv

t=fv

tool(hd(4));hd(5)=design(hf,'equiripple');hfvt=fvtool(hd(4:5));legend(hfvt,'kaiser window design,filter order 68','equirippledesign,filter order 53');

output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-100

-8 0

-6 0

-4 0

-2 0

0


M

agnitude

(dB)


kaiser w indow des ign,f i lter order 68

equiripple des ign,fi lter order 53


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Experiment No- 27

Object: write a program to filter order control

N=20

Percentage order =100 to 101Coefficients setspecs(hf, N,fc,Ap,Ast,N,,fc,Ap,Ast)

Program:

(i) filter order control :N=20;Setspecs (hf,'N,fc,ap,ast',N,fc,ap,ast);hd(6)=design(hf,'equiripple');hfvt=fvtool(hd(5:6));legend (hfvt,'equiripple design,53coefficents','equiripple design,20 coefficents' );

output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-100

-9 0

-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0


M

agnitu

de

(dB)


equiripple design,53 coefficents

equiripple design,20 coefficents


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ii) transition width control :

setspecs(hf,'N,fp,fst',N,fp,fst);hd(7)=design(hf,'equiripple');measure(hd(7));hfvt=fvtool(hd(5),hd(7));

legend(hfvt,'equiripple design,53coefficents','equiripple design,20 coefficents' );

output:

0 0.1 0 .2 0 .3 0.4 0 .5 0.6 0.7 0.8 0.9

-100

-9 0

-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0


M

agnitude

(dB)


equiripple design,53 coefficentsequiripple design,20 coefficents


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iii) Stop bend attenuation:

fc=0.6;

n=20;

hf=fdesign.lowpass('n,fc',n,fc);

fp=0.6;

fst=0.7725;

ap=0.01;

ast=90;

setspecs(hf,'N,fp,fst',N,fp,fst);

hd(8)=design(hf,'equiripple','wstop',(5));

measure(hd(8));

hfvt=fvtool(hd(7:8));

Output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0


M

agnitude

(dB)



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iv) Design containing:

fc=0.6;n=20;hf=fdesign.lowpass('n,fc',n,fc);fp=0.6;

fst=0.7725;ap=0.01;ast=90;setspecs(hf,'fp,fst,ap,ast',fp,fst,ap,ast);hd(9)=design(hf,'equiripple');hfvt=fvtool(hd(8:9));legend(hfvt,'equiripple design using weights','equirippledesign containing the stop band');

output:

0 0.1 0 .2 0 .3 0 .4 0 .5 0.6 0.7 0.8 0.9

-100

-9 0

-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0


M

agnitude

(dB)


equiripple design using w eights

equiripple design containing the stop band


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EXPERIMENT-28

Object: write a program for down sampler.

Program:

fs=9;t=[0:74]/fs;a1=input('enter the values of amplitude a1=');s1=a1*sin(2*pi*t*.42);subplot(1,2,1);stem(s1);xlabel('sinewave with f=.42Hz');ylabel('amplitude');fs=3;t=[0:74]/fs;s2=a1*sin(2*pi*t*.42);subplot(1,2,2);stem(s2);xlabel('sinewave with f=.42Hz');ylabel('amplitude');

Output:


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EXPERIMENT-29

Object: write a program for up sampler.

Program:

fs=9;t=[0:74]/fs;a1=input('enter the values of amplitude a1=');s1=a1*sin(2*pi*t*.12);subplot(1,2,1);stem(s1);xlabel('sinewave with f=.12Hz');ylabel('amplitude');s2=upsample(s1,3);subplot(1,2,2);stem(s2);xlabel('sinewave with f=.12Hz');ylabel('amplitude');

Output :

sp lab report

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