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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
if x(i)>=0y(i)=1else
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
endstem(x,y)xlabel('x-axis')ylabel('y-axis')
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
endstem(x,y)xlabel('x-axis')ylabel('y-axis')
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
if x(i)>=0y(i)=1else
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
Normalized Frequency (vT rad/sample)
M
agnitude(d
B)
Magnitude Response (dB)
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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
Normalized Frequency (vT rad/sample)
M
agnitude
(dB)
Magnitude Response (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
Normalized Frequency (vT rad/sample)
M
agnitu
de
(dB)
Magnitude Response (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
Normalized Frequency (vT rad/sample)
M
agnitude
(dB)
Magnitude Response (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
Normalized Frequency (vT rad/sample)
M
agnitude
(dB)
Magnitude Response (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
Normalized Frequency (vT rad/sample)
M
agnitude
(dB)
Magnitude Response (dB)
equiripple design using w eights
equiripple design containing the stop band
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8/3/2019 Sp Lab Report
49/50
49
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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8/3/2019 Sp Lab Report
50/50
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 :