SUM OF TWO SINUSOIDAL SIGNALS
Experiment No: - 01
AIM: - To write a MATLAB program to find the sum of two sinusoidal signals.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
Clear all;
Close all;
t=0:0.001:0.1;
f1=50;
x1=2*pi*f1*t;
y1=sin(x1);
figure;
subplot (3,1,1);
plot (t,y1);
title('sin(x1');
f2=100;
x2=2*pi*f2*t;
y2=sin(x2);
subplot(3,1,2);
plot(t,y2);
title('sin(x2)');
y=y1+y2;
subplot(3,1,3);
plot(t,y);
title('sinx1=sinx2')
RESULTS:Thus the MATLAB program for sum of two sinusoidal signals was performed and the output
was verified.
Page No 1
OUTPUT:
Page No 2
ANALOG LOW PASS FILTER
Experiment No: - 02(a)
AIM: - To write a MATLAB program to plot magnitude response of analog
Low pass filter.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
close all;
clear all;
f=100:20:8000;
fh=900;
k=length(f);
for i=1:k;
m(i)=1/sqrt(1+(f(i)/fh)^2);
mag(i)=20*log10(m(i));
end;
figure;
semilogx(f,mag);
title('magnitude response of analog of low pass filter')
xlabel('frequency----->');
ylabel('magnitude in db');
grid on;
RESULTS:Thus the MATLAB program for analog Low pass filter was written and magnitude response
was plotted.
Page No 3
OUTPUT:-
Page No 4
ANALOG HIGH PASS FILTER
Experiment No: - 02(b)
AIM: - TO write a MATLAB program to plot magnitude response of analog
High pass filter..
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
close all;
clear all;
f=100:20:8000;
fl=400;
k=length(f);
for i=1:k;
m(i)=1/sqrt(1+(fl/f(i))^2);
mag(i)=20*log10(m(i));
end;
figure;
semilogx(f,mag);
title('magnitude response of analog of high pass filter');
xlabel('frequency----->');
ylabel('magnitude in db');
grid on;
RESULTS:Thus the MATLAB program for analog high pass filter was written and magnitude response
was plotted.
Page No 5
OUTPUT:
-
Page No 6
FIR LP\HP FILTER
USING
KAISER WINDOWING TECHNIQUES
Experiment No: - 03(a)
AIM: - TO write a MATLAB program to design FIR LP\HP using Kaiser window
techniques.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
close all;
clear all;
format long;
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passband frequency');
fs=input('enter the stopband frequency');
f=input('enter the sampling frequency');
beta=input('enter the beta value');
wp=2*(fp/f);
ws=2*(fs/f);
num=-20*log10(sqrt(rp*rs))-13;
dem=14.6*(fs-fp)/f;
n=ceil(num/dem);
n1=n+1;
if(rem(n,2)~=0)
n1=n;
n=n-1;
end;
y=kaiser(n1,beta);
%Lowpass filter
b=fir1(n,wp,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,1);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Kaiser window of LPF ----');
grid on;
Page No 7
%Highpass filter
b=fir1(n,wp,'high',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));subplot(2,1,2);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Kaiser window of HPF ----');
grid on;
RESULTS:-
Thus the MATLAB program for FIR LP\HP using Kaiser Window
Techniques was executed.
INPUT:enter the pass band ripple
0.02
enter the stop band ripple
0.01
enter the pass band frequency 1000
enter the stop band frequency 1500
enter the sampling frequency 10000
enter the beta value
5.8
OUTPUT:
Page No 8
Page No 9
FIR LP\HP FILTER
USING
TRIANGULAR WINDOWING TECHNIQUES
Experiment No: - 03(b)
AIM: - TO write a MATLAB program to design FIR LP\HP using Triangular window
Techniques.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:
clc;
close all;
clear all;
format long;
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passband frequency');
fs=input('enter the stopband frequency');
f=input('enter the sampling frequency');
wp=2*(fp/f);
ws=2*(fs/f);
num=-20*log10(sqrt(rp*rs))-13;
dem=14.6*(fs-fp)/f;
n=ceil(num/dem);
n1=n+1;
if(rem(n,2)~=0)
n1=n;
n=n-1;
end;
y=triang(n1);
%Lowpass filter
b=fir1(n,wp,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,1);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Triangular window of LPF ----');
grid on;
Page No 10
%Highpass filter
b=fir1(n,wp,'high',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,2);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Triangular window of HPF ----');
grid on ;
RESULTS:Thus the MATLAB program for FIR LP\HP using triangular window
Techniques was executed.
INPUT:enter the passband ripple
enter the stopband ripple
enter the passband frequency
enter the stopband frequency
enter the sampling frequency
0.04
0.02
1500
2000
8000
Page No 11
OUTPUT:
Page No 12
FIR LP\HP FILTER
USING
RECTANGULAR WINDOWING TECHNIQUES
Experiment No: - 03(c)
AIM: - TO write a MATLAB program to design FIR LP\HP using Rectangular window
Techniques.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:
clc;
close all;
clear all;
format long;
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
fp=input('enter the passband frequency');
fs=input('enter the stopband frequency');
f=input('enter the sampling frequency');
wp=2*(fp/f);
ws=2*(fs/f);
num=-20*log10(sqrt(rp*rs))-13;
dem=14.6*(fs-fp)/f;
n=ceil(num/dem);
n1=n+1;
if(rem(n,2)~=0)
n1=n;
n=n-1;
end;
y=boxcar(n1);
%Lowpass filter
b=fir1(n,wp,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,1);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Rectangular window of LPF ----');
grid on;
Page No 13
%Highpass filter
b=fir1(n,wp,'high',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,2);
plot(o/pi,m);
ylabel('gain in db---->');
xlabel('Normalised frequency---->');
title('FIR filter using Rectangular window of HPF ----');
title('Magnitude response of high pass filter');
grid on;
RESULTS:Thus the MATLAB program for FIR LP\HP using rectangular window
Techniques was executed.
INPUT:enter the passband ripple
0.04
enter the stopband ripple
0.05
enter the passband frequency 1500
enter the stopband frequency 2000
enter the sampling frequency 9000
Page No 14
OUTPUT:
Page No 15
LINEAR CONVOLUTION USING MATLAB
Experiment No: - 04
AIM: - TO write a MATLAB program to compute linear convolution of two given
Sequences.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
clear all;
close;
disp('enter the length of the first sequence m=');
m=input('');
disp('enter the length of first sequence x[m]=');
for i=1:m
x(i)=input('');
end
disp('enter the length of the second sequence n=');
n=input('');
disp('enter the length of second sequence h[n]=');
for j=1:n
h(j)=input('');
end
y=conv(x,h);
figure;
subplot(3,1,1);
stem(x);
ylabel ('amplitude---->');
xlabel('n---->');
title('x(n) Vs n');
subplot(3,1,2);
stem(h);
ylabel('amplitude---->');
xlabel('n---->');
title('h(n) Vs n');
subplot(3,1,3);
stem(y);
ylabel('amplitude---->');
xlabel('n---->');
title('y(n) Vs n');
disp('linear convolution of x[m] and h[n] is y');
Page No 16
INPUT:-Enter the length of the first sequence m=
6
Enter the length of first sequence x[m]=
1
2
3
4
5
6
Enter the length of the second sequence n=
6
Enter the length of second sequence h[n]=
1
2
3
4
5
6
OUTPUT:Linear convolution of x[m] and h[n] is y=
1 4 10 20 35 56 70 76 73 60 36
RESULTS :- Thus the program for linear convolution is written using MATLAB and verified.
Page No 17
CIRCULAR CONVOLUTION USING MATLAB
Experiment No: - 05
AIM: - TO write a MATLAB program to compute Circular convolution of two given
Sequences.
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:RESULTS:Thus the program for circular convolution is written using MATLAB and verified.
INPUT:enter the 1st sequence[1 2 3 4 5 6 ]
enter the 2nd sequence[1 2 3 4 5]
Page No 18
OUTPUT:Circular convolution of x(m) and h(n) is y=
59 62 59 50 35 50
Page No 19
BUTTERWORTH LOW PASS FILTER
Experiment No: - 06(a)
AIM: - TO write a MATLAB program to Amplitude response and response of Butter worth Low pass filter
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
close all;
clear all;
format long;
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
wp=input('enter the passband frequency');
ws=input('enter the stopband frequency');
fs=input('enter the sampling frequency');
w1=2*wp/fs;
w2=2*ws/fs;
[n,wn]=buttord(w1,w2,rp,rs,'s');
[z,p,k]= butter(n,wn);
[b,a]=butter(n,wn,'s');
w=0:0.01:pi;
[h,om]=freqs(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
ylabel('gain in db--------->');
xlabel('(a) normalized freq------>');
subplot(2,1,2);
plot(om/pi,an);
ylabel('phase in db--------->');
xlabel('(b) normalized freq------>');
Page No 20
INPUT:enter the
enter the
enter the
enter the
enter the
RESULTS:-
passband
stopband
passband
stopband
sampling
ripple.15
ripple60
frequency1500
frequency3000
frequency7000
Thus the Amplitude response and phase response of Butter worth Low pass filter was verified.
OUTPUT:-
Page No 21
BUTTERWORTH HIGH PASS FILTER
Experiment No: - 06(b)
AIM: - TO write a MATLAB program to Amplitude response and response of Butter worth high pass filter
PROCEDURE:-
Open MATLAB
Open new M-file
Type the program
Save in current directory
Compile and Run the program
For the output see command window\ Figure window
PROGRAM:clc;
close all;
clear all;
format long;
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
wp=input('enter the passband frequency');
ws=input('enter the stopband frequency');
fs=input('enter the sampling frequency');
w1=2*wp/fs;
w2=2*ws/fs;
[n,wn]=buttord(w1,w2,rp,rs,'s');
[z,p,k]= butter(n,wn);
[b,a]=butter(n,wn,'high','s');
w=0:0.01:pi;
[h,om]=freqs(b,a,w);
m=20*log10(abs(h));
an=angle(h);
subplot(2,1,1);
plot(om/pi,m);
ylabel('gain in db--------->');
xlabel('(a) normalized freq------>');
subplot(2,1,2);
plot(om/pi,an);
ylabel('phase in db--------->');
xlabel('(b) normalized freq------>');
Page No 22
INPUT:Enter the
Enter the
Enter the
Enter the
Enter the
passband
stopband
passband
stopband
sampling
ripple.2
ripple40
frequency2000
frequency3500
frequency8000
RESULTS:Thus the Amplitude response and phase response of Butter worth high pass filter was verified.
OUTPUT:
Page No 23
LINER CONVOLUTION
Experiment No: - 07
AIM: - TO write a C- program to find linear convolution of given two sequences
Procedure to Work on Code Composer Studio
To create the New Project
Project→ New (File Name. pjt, Eg: Vectors.pjt)
To create a Source file
File →New→ Type the code (Save & give file name, Eg: sum.c).
To Add Source files to Project
Project→ Add files to Project→ sum.c
To Add rts.lib file & Hello.cmd:
Project→ Add files to Project→ rts6700.lib
Library files: rts6700.lib (Path: c:\ti\c6000\cgtools\lib\ rts6700.lib)
Note: Select Object& Library in (*.o,*.l) in Type of files
Project→ Add files to Project→hello.cmd
CMD file- Which is common for all non real time programs.
(Path: c:\ti \ tutorial\dsk6713\hello1\hello.cmd)
Note: Select Linker Command file (*.cmd) in Type of files
Compile:To Compile: Project→ Compile
To Rebuild: project → rebuild,
Which will create the final .out executable file. (Eg.Vectors.out).
Procedure to Lode and Run program:
Load the Program to DSK: File→ Load program →Vectors.out
To Execute project: Debug → Run
Page No 24
PROGRAM:#include<stdio.h>
int m=6;
int n=6;
int i=0,j;
int x[15]={1,2,3,4,5,6,0,0,0,0,0,0};
int h[15]={1,2,3,4,5,6,0,0,0,0,0,0};
int y[20];
main()
{
for(i=0;i<m+n-1;i++)
{
y[i]=0;
for(j=0;j<=i;j++)
y[i]+=x[j]*h[i-j];
}
for(i=0;i<m+n-1;i++)
printf("%d \n",y[i]);
}
RESULTS:- Thus the C- Program for Linear convolution was written
and the output was verified
OUTPUT:4
10
20
35
56
70
76
73
60
36
Page No 25
Page No 26
Page No 27
CIRCULAR CONVOLUTION
Experiment No: - 08
AIM: - TO write a C- program to find Circular convolution of given two sequences
Procedure to Work on Code Composer Studio
To create the New Project
Project→ New (File Name. pjt, Eg: Vectors.pjt)
To create a Source file
File →New→ Type the code (Save & give file name, Eg: sum.c).
To Add Source files to Project
Project→ Add files to Project→ sum.c
To Add rts.lib file & Hello.cmd:
Project→ Add files to Project→ rts6700.lib
Library files: rts6700.lib (Path: c:\ti\c6000\cgtools\lib\ rts6700.lib)
Note: Select Object& Library in (*.o,*.l) in Type of files
Project→ Add files to Project→hello.cmd
CMD file- Which is common for all non real time programs.
(Path: c:\ti \ tutorial\dsk6713\hello1\hello.cmd)
Note: Select Linker Command file (*.cmd) in Type of files
Compile:To Compile: Project→ Compile
To Rebuild: project → rebuild,
Which will create the final .out executable file. (Eg.Vectors.out).
Procedure to Lode and Run program:
Load the Program to DSK: File→ Load program →Vectors.out
To Execute project: Debug → Run
Page No 28
PROGRAM:#include<stdio.h>
int m,n,x[30],h[30],y[30],i,j,temp[30],k,x2[30],a[30];
void main()
{
printf("enter the length of the 1st sequence\n");
scanf("%d",&m);
printf("enter the length of the second sequence\n");
scanf("%d",&n);
printf("enter the 1st sequence\n");
for(i=0;i<m;i++)
scanf("%d",&x[i]);
printf("enter the second sequence\n");
for(j=0;j<n;j++)
scanf("%d",&h[j]);
if(m-n!=0)
{
if(m>n)
{
for(i=n;i<m;i++)
h[i]=0;
n=m;
}
for(i=m;i<n;i++)
x[i]=0;
m=n;
}
y[0]=0;
a[0]=h[0];
for(j=1;j<n;j++)
a[j]=h[n-j];
for(i=0;i<n;i++)
y[0]+=x[i]*a[i];
for(k=1;k<n;k++)
{
y[k]=0;
for(j=1;j<n;j++)
x2[j]=a[j-1];
x2[0]=a[n-1];
for(i=0;i<n;i++)
{
Page No 29
a[i]=x2[i];
y[k]+=x[i]*x2[i];
}
}
printf("the circular convolution is\n");
for(i=0;i<n;i++)
printf("%d\t",y[i]);
}
INPUT:enter the length of the 1st sequence
5
enter the length of the second sequence
5
enter the 1st sequence
1
2
3
4
5
enter the second sequence
1
2
3
4
5
OUTPUT:the circular convolution is
45
50
50
45
35
Page No 30
Page No 31
RESULTS:- Thus the C- Program for Circular convolution was written
and the output was verified
Page No 32
8 – FFT
Experiment No: - 09
AIM: - TO write a C- program to compute 8 – FFT of given sequences using DIF – FFT algorithm
Procedure to Work on Code Composer Studio
To create the New Project
Project→ New (File Name. pjt, Eg: Vectors.pjt)
To create a Source file
File →New→ Type the code (Save & give file name, Eg: sum.c).
To Add Source files to Project
Project→ Add files to Project→ sum.c
To Add rts.lib file & Hello.cmd:
Project→ Add files to Project→ rts6700.lib
Library files: rts6700.lib (Path: c:\ti\c6000\cgtools\lib\ rts6700.lib)
Note: Select Object& Library in (*.o,*.l) in Type of files
Project→ Add files to Project→hello.cmd
CMD file- Which is common for all non real time programs.
(Path: c:\ti \ tutorial\dsk6713\hello1\hello.cmd)
Note: Select Linker Command file (*.cmd) in Type of files
Compile:To Compile: Project→ Compile
To Rebuild: project → rebuild,
Which will create the final .out executable file. (Eg.Vectors.out).
Procedure to Lode and Run program:
Load the Program to DSK: File→ Load program →Vectors.out
To Execute project: Debug → Run
Page No 33
PROGRAM:#include<stdio.h>
#include<math.h>
#define N 8
#define PI 3.14159
typedef struct
{
float real,imag;
}
complex;
main()
{
int i;
complex w[N];
complex x[8]={0,0.0,1,0.0,2,0.0,3,0.0,4,0.0,5,0.0,6,0.0,7,0.0};
complex temp1,temp2;
int j,k,upper_leg,lower_leg,leg_diff,index,step;
for(i=0;i<N;i++)
{
w[i].real=cos((2*PI*i)/(N*2.0));
w[i].imag=-sin((2*PI*i)/(N*2.0));
}
leg_diff=N/2;
step=2;
for(i=0;i<3;i++)
{
index=0;
for(j=0;j<leg_diff;j++)
{
for(upper_leg=j;upper_leg<N;upper_leg+=(2*leg_diff))
{
lower_leg=upper_leg+leg_diff;
temp1.real=(x[upper_leg]).real+(x[lower_leg]).real;
temp1.imag=(x[upper_leg]).imag+(x[lower_leg]).imag;
temp2.real=(x[upper_leg]).real-(x[lower_leg]).real;
temp2.imag=(x[upper_leg]).imag-(x[lower_leg]).imag;
(x[lower_leg]).real=temp2.real*(w[index]).real-temp2.imag*(w[index]).imag;
(x[lower_leg]).imag=temp2.real*(w[index]).imag+temp2.imag*(w[index]).real;
(x[upper_leg]).real=temp1.real;
(x[upper_leg]).imag=temp1.imag;
}
index+=step;
}
Page No 34
leg_diff=(leg_diff)/2;
step=step*2;
}
j=0;
for(i=1;i<(N-1);i++)
{
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
j=j+k;
if(i<j)
{
temp1.real=(x[j]).real;
temp1.imag=(x[j]).imag;
(x[j]).real=(x[i]).real;
(x[j]).imag=(x[i]).imag;
(x[i]).real=temp1.real;
(x[i]).imag=temp1.imag;
}
}
printf("the fft of the given input sequence is \n");
for(i=0;i<8;i++)
{
printf("%f %f \n",(x[i]).real,(x[i]).imag);
}
}
OUTPUT:the fft of the given input sequence is:
28.000000 0.000000
-4.000012 9.656858
-4.000005 4.000000
-4.000010 1.656851
-4.000000 0.000000
-3.999998 -1.656858
-3.999995 -4.000000
-3.999980 -9.656851
Page No 35
FFT 1-D
Experiment No: - 10
AIM: - TO write a C- program to compute FFT of the given 1- D signal and plot
Algorithm:1.
2.
3.
4.
5.
Select no. of points for FFT
Generate a sine wave of frequency ‘f’.
Take sampled data and apply FFT algorithm.
Use Graph option to view the input and output.
Repeat step 1to 4 for different no. of points and frequencies.
PROGRAM:-
#include<stdio.h>
#include<math.h>
#define N 32
#define PI 3.14159
typedef struct
{
float real,imag;
}
complex;
float iobuffer[N];
float y[N];
main()
{
int i;
complex w[N];
complex x[N];
complex temp1,temp2;
int j,k,upper_leg,lower_leg,leg_diff,index,step;
for(i=0;i<N;i++)
{
iobuffer[i]=sin((2*PI*2*i)/32.0);
}
for(i=0;i<N;i++)
{
Page No 36
x[i].real=iobuffer[i];
x[i].imag=0.0;
}
for(i=0;i<N;i++)
{
w[i].real=cos((2*PI*i)/(N*2.0));
w[i].imag=-sin((2*PI*i)/(N*2.0));
}
leg_diff=N/2;
step=2;
for(i=0;i<5;i++)
{
index=0;
for(j=0;j<leg_diff;j++)
{
for(upper_leg=j;upper_leg<N;upper_leg+=(2*leg_diff))
{
lower_leg=upper_leg+leg_diff;
temp1.real=(x[upper_leg]).real+(x[lower_leg]).real;
temp1.imag=(x[upper_leg]).imag+(x[lower_leg]).imag;
temp2.real=(x[upper_leg]).real-(x[lower_leg]).real;
temp2.imag=(x[upper_leg]).imag-(x[lower_leg]).imag;
(x[lower_leg]).real=temp2.real*(w[index]).real-temp2.imag*(w[index]).imag;
(x[lower_leg]).imag=temp2.real*(w[index]).imag+temp2.imag*(w[index]).real;
(x[upper_leg]).real=temp1.real;
(x[upper_leg]).imag=temp1.imag;
}
index+=step;
}
leg_diff=(leg_diff)/2;
step=step*2;
}
j=0;
for(i=1;i<(N-1);i++)
{
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
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j=j+k;
if(i<j)
{
temp1.real=(x[j]).real;
temp1.imag=(x[j]).imag;
(x[j]).real=(x[i]).real;
(x[j]).imag=(x[i]).imag;
(x[i]).real=temp1.real;
(x[i]).imag=temp1.imag;
}
}
for(i=0;i<N;i++)
{
y[i]=sqrt((x[i].real*x[i].real)+(x[i].imag*x[i].imag));
}
for(i=0;i<N;i++)
{
printf("%f\t",y[i]);
}
return(0);
}
OUTPUT:-
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POWER DENSITY SPECTRUM
Experiment No: - 11
AIM: - TO write a C- program to compute power density spectrum of given one – dimensional signal and plot.
Algorithm:1 Select no. of points for FFT
2 Generate a sine wave of frequency ‘f’.(Sampling rate = No. of points of FFT)
3 Compute the Auto Correlation of sine wave.
4 Take output of auto correlation, apply FFT algorithm.
5 Use Graph option to the PDS. .
6. Repeat step 1to 4 for different no. of points and frequencies.
PROGRAM:-
#include<stdio.h>
#include<math.h>
#define N 16
#define PI 3.14159
typedef struct
{
float real,imag;
}
complex;
complex x[N];
float iobuffer[N];
float x1[N],y[N];
int i;
main()
{
complex w[N];
complex temp1,temp2;
float sum=0.0;
int j,k,n,upper_leg,lower_leg,leg_diff,index,step;
for(i=0;i<N;i++)
{
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iobuffer[i]=sin((2*PI*2*i)/15.0);
}
for(n=0;n<N;n++)
{
sum=0;
for(k=0;k<N-n;k++)
{
sum=sum+(iobuffer[k]*iobuffer[n+k]);
}
x1[n]=sum;
}
for(i=0;i<N;i++)
{
x[i].real=x1[i];
x[i].imag=0.0;
}
for(i=0;i<N;i++)
{
w[i].real=cos((2*PI*i)/(N*2.0));
w[i].imag=-sin((2*PI*i)/(N*2.0));
}
leg_diff=N/2;
step=2;
for(i=0;i<4;i++)
{
index=0;
for(j=0;j<leg_diff;j++)
{
for(upper_leg=j;upper_leg<N;upper_leg+=(2*leg_diff))
{
lower_leg=upper_leg+leg_diff;
temp1.real=(x[upper_leg]).real+(x[lower_leg]).real;
temp1.imag=(x[upper_leg]).imag+(x[lower_leg]).imag;
temp2.real=(x[upper_leg]).real-(x[lower_leg]).real;
temp2.imag=(x[upper_leg]).imag-(x[lower_leg]).imag;
(x[lower_leg]).real=temp2.real*(w[index]).real-temp2.imag*(w[index]).imag;
(x[lower_leg]).imag=temp2.real*(w[index]).imag+temp2.imag*(w[index]).real;
(x[upper_leg]).real=temp1.real;
(x[upper_leg]).imag=temp1.imag;
}
index+=step;
}
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leg_diff=(leg_diff)/2;
step=step*2;
}
j=0;
for(i=1;i<(N-1);i++)
{
k=N/2;
while(k<=j)
{
j=j-k;
k=k/2;
}
j=j+k;
if(i<j)
{
temp1.real=(x[j]).real;
temp1.imag=(x[j]).imag;
(x[j]).real=(x[i]).real;
(x[j]).imag=(x[i]).imag;
(x[i]).real=temp1.real;
(x[i]).imag=temp1.imag;
}
}
for(i=0;i<N;i++)
{
y[i]=sqrt((x[i].real*x[i].real)+(x[i].imag*x[i].imag));
}
for(i=0;i<N;i++)
{
printf("%f\t",y[i]);
}
return(0);
}
OUTPUT:-
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