A practical report on Digital Signal Processing and Control System under MATLAB Environment present in M.Tech 1st Semester during session 2013-14.

1. A
Practical Report
on
DIGITAL SIGNAL PROCESSING
&
CONTROL SYSTEM
Under MATLAB Environment
Submitted To:
Mr. Asim Ali Khan
Associate Professor
Mr. Manpreet Singh Manna
Associate Professor
Submitted By:
Paramjeet Singh Jamwal
PG/ICE/136321
M.Tech
First Semester
DEPARTMENT OF ELECTRICAL AND INSTRUMENTATION ENGINEERING
SANT LONGOWAL INSTITUTE OF ENGINEERING & TECHNOLOGY
LONGOWAL - 148106
JAN 2014
1|Page
info4eee | MATLAB

2. S.No.
1.
2.
3.
4.
5.
6.
7.
Command
Clc
clear all
close all
zeros(N)
zeros(M,N)
ones(N)
ones(M,N)
8.
subplot(m,n,p)
9.
stem(y)
10.
11.
12.
stem(x,y)
xlabel(‘text’)
ylabel(‘text’)
Input(‘How many
assignments’)
sum(A)
prod(A)
mean(A)
length(A)
inv(A)
A’
rand(N)
rand(N,M)
magic(N)
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
max(A)
min(A)
Function
Clear command window and homes the cursors
Removes all variables, globals, functions and MEX links.
Closes all the open figure windows.
An N-by-N matrix of zeros.
An M-by-N matrix of zeros.
An N-by-N matrix of ones.
An M-by-N matrix of ones.
Breaks the Figure window into an m-by-n matrix of small
axes, selects the p-th axes for the current plot, and returns the
axis handle.
Plots the data sequence y as stems from the x axis terminated
with circles for the data value. If y is a matrix then each
column is plotted as a separate series.
Plots the data sequence y at the values specified in x.
Adds text beside the x-axis on the current axis.
Adds text beside the y-axis on the current axis.
To get user defined value
To find sum of matrix ‘A’ column wise.
To find product of ‘A’(column wise).
Find mean of ‘A’.
To find length of matrix ‘A’.
To find inverse of matrix ‘A’ if possible.
It gives transpose of matrix ‘A’.
It generates N-N random matrix.
It generates N-M random matrix.
It generates N-N matrix whose sum of all rows and columns
are equal.
It shows largest element present in each column.
It shows smallest element present in each column.
2|Page
info4eee | MATLAB

3. 1. Write a program to generate unit step signal.
Program:
n=input('enter lowest index= ');
m=input('enter highest index= ');
t=n:m;
x=ones(1,m-n+1);
stem(t,x);
axis([n m 0 1.5]);
title('Unit Step Signal')
xlabel('Value of n')
ylabel('Amplitude')
Command Window:
>> psj_unitstep
enter lowest index= 7
enter highest index= 17
Figure Window:
3|Page
info4eee | MATLAB

4. 2. Write a program to generate ramp signal.
Program:
n=input('enter lowest index= ');
m=input('enter highest index= ');
t=n:m;
x=0:m-n;
stem(t,x);
axis([n m 0 m-n+1]);
title('Unit Ramp Signal')
xlabel('Value of n')
ylabel('Amplitude')
Command Window:
>> psj_unitramp
enter lowest index= 7
enter highest index= 17
Figure Window:
4|Page
info4eee | MATLAB

5. 3. Write a program to generate unit impulse signal.
Program:
n=input('enter the value of impluse point= ');
t=n-2:n+2;
x=[zeros(1,2) ones(1,1) zeros(1,2)];
stem(t,x);
axis([n-2 n+2 0 1.5]);
title('Unit Impulse Signal')
xlabel('Value of n')
ylabel('Amplitude')
Command Window:
>> psj_unitimpulse
enter the value of impluse point= 7
Figure Window:
5|Page
info4eee | MATLAB

6. 4. Write a program to find the convolution of two numbers.
Program:
x=input('Enter the value of x= ');
h=input('Enter the value of h= ');
lx=length(x);
lh=length(h);
z(1,1:lx+lh-1)=zeros;
l=max(lx,lh);
for i=1:l
y(1,2*i-1)=x(1,i)*h(1,i);
z(1,2*i-1)=z(1,2*i-1)+y(1,2*i-1);
end
for j=2:l
for i=j:l
y(1,2*i-j)=x(1,i)*h(1,i-j+1)+x(1,i-j+1)*h(1,i);
z(1,2*i-j)=z(1,2*i-j)+y(1,2*i-j);
end
end
disp('The Convolution of x & h is');
z
Command Window:
>> psj_convolution
Enter the value of x= [2,-1,0,0,1,0,-1]
Enter the value of h= [1,2,2,1,0,-1,0]
The Convolution of x & h is
z=
2
3
2
0
0
0
2
-1
-2
-2
0
1
0
6|Page
info4eee | MATLAB

7. 5. Write a program to generate cosine wave of different amplitude.
Program:
t=0:0.01:10;
c1=0.5*cos(2*pi*t);
c2=cos(4*pi*t);
c3=(2/3)*cos(6*pi*t);
c=1+c1+c2+c3;
subplot(4,1,1),plot(t,c1);
xlabel('time axis----->'),ylabel('Amplitude----->');
axis([0 10 -0.7 0.7]);
title('0.5*cos(2*pi*t)')
subplot(4,1,2),plot(t,c2);
xlabel('time axis----->'),ylabel('Amplitude----->');
title('cos(4*pi*t)')
axis([0 10 -1.2 1.2]);
subplot(4,1,3),plot(t,c3);
xlabel('time axis----->'),ylabel('Amplitude----->');
title('(2/3)*cos(6*pi*t)')
subplot(4,1,4),plot(t,c);
xlabel('time axis----->'),ylabel('Amplitude of c----->');
title('1+0.5*cos(2*pi*t)+cos(4*pi*t)+(2/3)*cos(6*pi*t)')
Command Window:
>> psj_cosine
7|Page
info4eee | MATLAB

8. Figure Window:
8|Page
info4eee | MATLAB

9. 6. Inbuilt function for Fourier transform in MATLAB.
S.No.
Command
FFT(X)
1.
FFT(X,N)
FFT(X,N,DIM)
FFT2(X)
2.
FFT2(X,MROWS,NCOLS)
FFTN(X)
3.
FFTN(X,SIZ)
IFFT(X)
IFFT(X,N)
IFFT(X,N,DIM)
4.
IFFT(..., 'symmetric')
IFFT(..., 'nonsymmetric')
IFFT2(F)
IFFT2(F,MROWS,NCOLS)
5.
IFFT2(..., 'symmetric')
IFFT2(..., 'nonsymmetric')
IFFTN(F)
6.
IFFTN(F,SIZ)
Function
Discrete Fourier transform (DFT) of vector X. For
matrices, the FFT operation is applied to each
column. For N-D arrays, the FFT operation operates
on the first non-singleton dimension.
N-point FFT padded with zeros if X has less than N
points and truncated if it has more.
FFT operation across the dimension DIMs.
Two-dimensional Fourier transform of matrix X. If
X is a vector, the result will have the same
orientation.
Pads matrix X with zeros to size MROWS-byNCOLS before transforming.
N-dimensional discrete Fourier transform of the N-D
array X. If X is a vector, the output will have the
same orientation.
Pads X so that its size vector is SIZ before
performing the transform. If any element of SIZ is
smaller than the corresponding dimension of X, then
X will be cropped in that dimension.
Inverse discrete Fourier transform of X.
N-point inverse transform.
Inverse discrete Fourier transform of X across the
dimension DIM.
IFFT to treat X as conjugate symmetric along the
active dimension. This option is useful when X is
not exactly
conjugate symmetric merely because of round-off
error.
IFFT to make no assumptions about the symmetry of
X.
Two-dimensional inverse Fourier transform of
matrix F. If F is a vector, the result will have the
same orientation.
Pads matrix F with zeros to size MROWS-byNCOLS before transforming.
IFFT2 to treat F as conjugate symmetric in two
dimensions so that the output is purely real. This
option is useful when F is not exactly conjugate
symmetric merely because of round-off error.
IFFT2 to make no assumptions about the symmetry
of F.
N-dimensional inverse discrete Fourier transform of
the N-D array F. If F is a vector, the result will have
the same orientation.
Pads F so that its size vector is SIZ before
performing the transform. If any element of SIZ is
9|Page
info4eee | MATLAB

10. IFFTN(..., 'symmetric')
IFFTN(..., 'nonsymmetric')
7.
DFTMTX(N)
CONJ(DFTMTX(N))/N
S = SPECTROGRAM(X)
S = SPECTROGRAM(X,WINDOW)
8.
S=
SPECTROGRAM(X,WINDOW,NOV
ERLAP)
S=
SPECTROGRAM(X,WINDOW,NOV
ERLAP,NFFT)
S=
SPECTROGRAM(X,WINDOW,NOV
ERLAP,NFFT,Fs)
[S,F,T] = SPECTROGRAM(...)
[S,F,T] =
smaller than the corresponding dimension of F, then
F will be cropped in that dimension.
IFFTN to treat F as multidimensionally conjugate
symmetric so that the output is purely real. This
option is useful when F is not exactly conjugate
symmetric merely because of round-off error.
IFFTN to make no assumptions about the symmetry
of F.
N-by-N complex matrix of values around the unitcircle whose inner product with a column vector of
length N yields the discrete Fourier transform of the
vector. If X is a column vector of length N, then
DFTMTX(N)*X yields the same result as FFT(X);
however, FFT(X) is more efficient.
The inverse discrete Fourier transform matrix.
Spectrogram of the signal specified by vector X in
the matrix S. By default, X is divided into eight
segment with 50% overlap, each segment is
windowed with a Hamming window. The number of
frequency points used to calculate the discrete
Fourier transforms is equal to the maximum of 256
or the next power of two greater than the length of
each segment of X. If X cannot be divided exactly
into eight segments, X will be truncated accordingly.
when WINDOW is a vector, divides X into
segments of length equal to the length of WINDOW,
and then windows each segment with the vector
specified in WINDOW. If WINDOW is an integer,
X is divided into segments of length equal to that
integer value, and a Hamming window of equal
length is used. If WINDOW is not specified, the
default is used.
the number of samples each segment of X overlaps.
NOVERLAP must be an integer smaller than
WINDOW if WINDOW is an integer. NOVERLAP
must be an integer smaller than the length of
WINDOW if WINDOW is a vector.
If
NOVERLAP is not specified, the default value is
used to obtain a 50% overlap.
specifies the number of frequency points used to
calculate the discrete Fourier transforms. If NFFT is
not specified, the default NFFT is used.
Fs is the sampling frequency specified in Hz. If Fs is
specified as empty, it defaults to 1 Hz. If it is not
specified, normalized frequency is used.
a vector of frequencies F and a vector of times T at
which the spectrogram is computed. F has length
equal to the number of rows of S. T has length k and
its value corresponds to the center of each segment.
where F is a vector of frequencies in Hz computes
10 | P a g e
info4eee | MATLAB

11. SPECTROGRAM(X,WINDOW,NOV
ERLAP,F,Fs)
[S,F,T,P] = SPECTROGRAM(...)
SPECTROGRAM(...)
9.
[X,T] =
INSTDFFT(XHAT,LOWB,UPPB)
10
[XHAT,OMEGA] =
NSTDFFT(X,LOWB,UPPB)
the spectrogram at those frequencies using the
Goertzel algorithm. The specified frequencies in F
are rounded to the nearest DFT bin commensurate
with the signal's resolution.
P is a matrix representing the Power Spectral
Density (PSD) of each segment. For real signals,
SPECTROGRAM returns the one-sided modified
periodogram estimate of the PSD of each segment;
for complex signals and in the case when a vector of
frequencies is specified, it returns the two-sided
PSD.
The PSD estimate for each segment on a surface in
the current figure with no output arguments. It uses
SURF(f,t,10*log10(abs(P)) where P is the fourth
output argument. A trailing input string,
FREQLOCATION, controls where MATLAB
displays the frequency axis. This string can be either
'xaxis' or 'yaxis'. Setting this FREQLOCATION to
'yaxis' displays frequency on the y-axis and time on
the x-axis. The default is 'xaxis' which displays the
frequency on the x-axis. If FREQLOCATION is
specified when output arguments are requested, it is
ignored.
the inverse nonstandard FFT of XHAT, on a powerof-2 regular grid (non necessarily integers) on the
interval [LOWB,UPPB]. Output arguments are X
the recovered signal computed on the time interval T
given by T = LOWB + [0:n-1]*(UPPB-LOWB)/n,
where n is the length of XHAT. Outputs are vectors
of length n. The length of XHAT must be a power of
2.
a nonstandard FFT of signal X sampled on a powerof-2 regular grid (non necessarily integers) on the
interval [LOWB,UPPB]. Output arguments are
XHAT the shifted FFT of computed on the interval
OMEGA given by OMEGA = [-n:2:n-2]/(2*(UPPBLOWB)) where n is the length of X. Outputs are
vectors of length n. Length of X must be a power of
2.
11 | P a g e
info4eee | MATLAB

12. 7. Write a program to find the Fourier transform of cosine function.
Program:
t=0:0.01:10;
x=cos(2*pi*t);
y=fft(x);
z=ifft(y);
subplot(3,1,1);
plot(x);
title('Cosine Wave')
subplot(3,1,2);
plot(y);
title('FFT of Cosine Wave')
subplot(3,1,3);
plot(z);
title('IFFT')
Command Window:
>> psj_fourier
Figure Window:
12 | P a g e
info4eee | MATLAB

13. 8. Write a program to find the DFT of given sequence.
Program:
h=input('enter sequence= ');
N=input('enter N=');
n=length(h);
x=[h,zeros(1,N-n)];
y=zeros(N,1);
for k=1:N,
for n=1:N,
y(k)=y(k)+x(n)*exp(-i*2*pi*(k-1)*(n-1)/N);
end
end
disp('DFT of x=');
y
Command Window:
>> psj_dft
enter sequence= [1 2 4 8 16 32 64 128]
enter N=8
DFT of x=
y=
1.0e+002 *
2.5500
0.4864 + 1.6607i
-0.5100 + 1.0200i
-0.7864 + 0.4607i
-0.8500 - 0.0000i
-0.7864 - 0.4607i
-0.5100 - 1.0200i
0.4864 - 1.6607i
13 | P a g e
info4eee | MATLAB

14. 9. Write a program to find the IDFT of given sequence.
Program:
h=input('enter sequence = ');
N=input('enter N = ');
n=length(x);
x=[h,zeros(1,N-n)];
y=zeros(N,1);
for n=1:N,
for k=1:N,
y(k)=y(k)+(1/N)*x(n)*exp(i*2*pi*(k-1)*(n-1)/N);
end
end
disp('IDFT of Sequence = ');
y
Command Window:
>> psj_idft
enter sequence = [36 -4+9.656i -4+4i -4+1.656i -4 -4-1.656i -4-4i -4-9.656i]
enter N = 8
IDFT of Sequence =
y=
1.0000
2.0003 + 0.0000i
3.0000 + 0.0000i
4.0003
5.0000 - 0.0000i
5.9997 - 0.0000i
7.0000 + 0.0000i
7.9997 - 0.0000i
14 | P a g e
info4eee | MATLAB

15. 10. Write a program to find the DFT of given sequence using matrix.
Program:
x=input('Enter the sequence = ');
n=length(x);
w=dftmtx(n);
y=[w*x'];
w;
disp('DFT of Sequence');
y
Command Window:
>> psj_dftumtx
Enter the sequence = [1 2 3 4 4 3 2 1]
DFT of Sequence
y=
20.0000
-5.8284 - 2.4142i
0
-0.1716 - 0.4142i
0
-0.1716 + 0.4142i
0
-5.8284 + 2.4142
15 | P a g e
info4eee | MATLAB

16. 11. Write a program to find the IDFT using matrix.
Program:
x=input('enter the sequence = ');
n=length(x);
w=conj(dftmtx(n))/n;
y=[inv(w)*x']/n;
w;
disp('IDFT of Sequence');
y
Command Window:
>> psj_idftumtx
enter the sequence = [36 -4+9.656i -4+4i -4+1.656i -4 -4-1.656i -4-4i -49.656i]
IDFT of Sequence
y=
1.0000 + 0.0000i
2.0003 + 0.0000i
3.0000 - 0.0000i
4.0003 - 0.0000i
5.0000 + 0.0000i
5.9997 + 0.0000i
7.0000 - 0.0000i
7.9997 + 0.0000i
16 | P a g e
info4eee | MATLAB

17. 12. Write a program to generate DFT Matrix without using direct command.
Program:
N=input('Enter the value of N = ');
x=zeros(N,N);
for j=1:N,
n=N*(j-1);
for k=1:N,
x(k+n)=exp(-i*2*pi*(j-1)*(k-1)/N);
end
end
disp('Resultant matrix ');
x
Command Window:
>> psj_dftmtx
Enter the value of N = 4
Resultant matrix
x=
1.0000
1.0000
1.0000
1.0000
1.0000
0.0000 - 1.0000i
-1.0000 - 0.0000i
-0.0000 + 1.0000i
1.0000
-1.0000 - 0.0000i
1.0000 + 0.0000i
-1.0000 - 0.0000i
1.0000
-0.0000 + 1.0000i
-1.0000 - 0.0000i
0.0000 - 1.0000i
17 | P a g e
info4eee | MATLAB

18. 13. Write a program to find the step response and impulse response of transfer
function.
Program:
sys=tf([8 18 31],[1 6 14 24])
subplot(2,1,1)
step(sys)
subplot(2,1,2)
impulse(sys)
Command Window:
>> psj_sni
Transfer function:
8 s^2 + 18 s + 31
----------------------s^3 + 6 s^2 + 14 s + 24
Figure Window:
18 | P a g e
info4eee | MATLAB

19. 14. Design a system to convert Fahrenheit to degree Celsius.
Setup:
19 | P a g e
info4eee | MATLAB

20. 15. Design a system for torque converter.
Setup:
-------------------------------------A
Group
--------------------------------------
20 | P a g e
info4eee | MATLAB