matlab programs re

8/8/2019 Matlab Programs Re

http://slidepdf.com/reader/full/matlab-programs-re 1/13

MATLAB PROGRAMS

% ALIASING

clc;

clear all;

t=-10:0.01:10;

T=4; fm=1/T;

x=cos(2*pi*fm*t);

fs1=1.6*fm;

fs2=2*fm;

fs3=8*fm;

n1=-4:1:4;

xn1=cos(2*pi*n1*fm/fs1);

subplot(2,2,1);

plot(t,x);

xlabel('time in sec');

ylabel('x(t)');

title('continious time signal');

subplot(2,2,2);

stem(n1,xn1,'-r');

hold on

plot(n1,xn1);

xlabel('time in sec');

ylabel('x(t)');

title('Discrete time signal with fs<2fm');

n2=-5:1:5;


subplot(2,2,3);

sampling frequency lesthan 2fm

sampling frequency equal to 2Fm

sampling frequency greater than 2Fm

n1 value ranges from -4 t0 4

signal with samp freq <2fm

didvides the entire plot into 2 rows and 2 coloumns, and plot the graph in first position

didvides the entire plot into 2 rows and 2 coloumns, and plot the graph in second position

used for ploting the values of t and X in continious form

to show the label in x axis in the figure

to show the label in Y axis in the figure

it gives the title for the figure displayed

used for ploting the values of t and X in discrete form

hold the values as it is

n2 value ranges from -5 t0 5 , i.e n2 = -5,-4,-3,-2,-1,0,1,2,3,4,5

signal with samp freq =2fm

didvides the entire plot into 2 rows and 2 coloumns, and plot the graph in third position



plot(n2,xn2,'-r');

hold on

stem(n2,xn2,'*g');

xlabel('n');

ylabel('x(n)');

title('Discrete time signal with fs=2fm');

n3=-20:1:20;


subplot(2,2,4);

plot(n3,xn3);

hold on

stem(n3,xn3,'-r');

xlabel('n');

ylabel('x(n)');

title('Discrete time signal with fs>2fm');

%LINEAR CONVOLUTION

clc;

clear all;

close all;

a=input('enter the 1 seq');

x=input('enter the 2 seq');

b=length(a);

c=x*convmtx(a,b);

disp(c);

l1=0:length(a)-1;

used for ploting the values of n2 and Xn2 in continious form where 'r' represents red colour

used for ploting the values of n2 and Xn2 in discrete form where 'g' represents green colour

signal with samp freq > 2fm

used for ploting the values of n3 and Xn3 in continious

closes the unnecessarywindow

get the 1st sequence at run time

get the 2nd sequence at run time

to find the length of a andstore it in 'b'

used to convolute thesequences a & x

it displays the value of c in comand window



subplot(1,3,1);

stem(l1,a);

xlabel('time');

ylabel('amp');

title('first input sequence');

l2=0:length(x)-1;

subplot(1,3,2);

stem(l2,x);

xlabel('time');

ylabel('amp');

title('second input sequence');

l3=0:length(c)-1;

subplot(1,3,3);

stem(l3,c);

xlabel('time');

ylabel('amp');

title('linear convolution of two sequences');

AT RUN TIME:

Enter the first sequence:[1 2 3 4]

Enter the second sequence:[3 2 1 4]

%CIRCULAR CONVOLUTION

clc;

clear all;

close all;

a=input('enter the first sequence');

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



c=ifft(fft(a).*fft(x));

disp('the convoluted sequence');

disp(c);

l1=0:length(a)-1;

subplot(1,3,1);

stem(l1,a);

ylabel('amp');

title('the first squence');

l2=0:length(x)-1;

subplot(1,3,2);

stem(l2,x);

xlabel('time');

ylabel('amp');

title('the second sequence');

l3=0:length(c)-1;

subplot(1,3,3);

st(l3,c);

xlabel('time');

ylabel('amp');

title('circular convolution');

AT RUNTIME

enter the first sequence[1 2 3 4]

enter the second sequence[4 3 2 1]

the convoluted sequence

24 22 24 30

derived from the circular convolution property of DFT



% DOWN SAMPLING

clear all;

N=50;

n=0:1:N-1;

x=sin(2*pi*n/20)+sin(2*pi*n/15);

m=2;

x1=x(1:m:N);

n1=1:1:N/m;

subplot(2,1,1);

stem(n,x);

xlabel('n');

ylabel('X');

title('input sequence');

subplot(2,1,2);

stem(n1,x1);

xlabel('n1');

ylabel('x1');

title('down unsampled sequence');

%ILLUSTRATION OF UP SAMPLING

clear all;

N=10;

n=0:1:N-1;

x=sin(2*pi*n/10)+sin(2*pi*n/5);

L=3;

x1=[zeros(1,L*N)]; here L*N = 30; so it returns the value zero from the range 1 to 30



n1=1:1:L*N; j=1:L:L*N;

x1(j)=x;

subplot(2,1,1);

stem(n,x);

xlabel('n');

ylabel('X');

title('input sequence');

subplot(2,1,2);

stem(n1,x1);

xlabel('n1');

ylabel('x1');

title('up unsampled sequence');

%BUTTERWORTH LPF

clc;

clear all;

close all;

format long;

rp=input('enter the passband ripple:');

rs=input('enter the stop band ripple');

wp=input('enter the pass band frequency');

ws=input('enter the stop band frequency');

fs=input('enter the sampling frequency');

w1=2*wp/fs;

w2=2*ws/fs;

[n,wn]=buttord(w1,w2,rp,rs); used to find the order of the filter 'n' and cutoff freq wn



[b,a]=butter(n,wn);

wn=(w1*w2);

wn=0:0.01:pi;

[h,o]=freqz(b,a,wn);

m=20*log10(abs(h));

an=angle(h);

subplot(2,1,1);

plot(o/pi,m);

xlabel('gain in db');

ylabel('normalised frequency');

subplot(2,1,2);

plot(o/pi,an);

xlabel('normalised freqz');

ylabel('phase in radians');

AT RUNTIME:

enter the passband ripple:.4

enter the stop band ripple30

enter the pass band frequency400

enter the stop band frequency800

enter the sampling frequency2000

% FFT sequence

clc;

clear all;

close all;

a=input('enter the input sequence');

used to find the transfer fncoefficients a and b



N=length(a);

for k=1:N

z(k)=0;

for n=1:N

z(k)=z(k)+[a(n)*exp(-j)*2*pi*(k-1)*(n-1)/n];

end;

c=abs(z);

d=angle(z);

l1=0:length(a)-1;

subplot(2,2,1);

stem(l1,a);

xlabel('time');

ylabel('amp');

title('the input sequence');

l2=0:length(z)-1;

subplot(2,2,2);

stem(l2,z);

xlabel('time');

ylabel('amp');

title('the fft of sequences');

l3=0:length(c)-1;

subplot(2,2,3);

stem(l3,c);

xlabel('time');

ylabel('amp');

title('the magnitude sequence');

l4=0:length(d)-1;



subplot(2,2,4);

stem(l4,d);

xlabel('time');

ylabel('amp');

title('the phase angle sequence');

end;

AT RUNTIME:

Enter the sequence: [1 2 3 4 5]

% FIR LPF USING WINDOWS

clc;

clear all;

wc=.5*pi;

N=25;

alpha=(N-1)/2;

eps=.001;

n=0:1:N-1;

hd=sin(wc*(n-alpha+eps))./(pi*(n-alpha+eps));

wr=boxcar(N); % rectangular window sequence

hn=hd.*wr';%filter coefficients

w=0:.01:pi;

h=freqz(hn,1,w);

plot(w/pi,abs(h),'-r');

hold on

wh=hamming(N); % rectangular window

hn=hd.*wh'; %filter coefficients

w=0:.01:pi;



h=freqz(hn,1,w);

plot(w/pi,abs(h),'-k');

hold on

wb=blackman(N);

hn=hd.*wb'; %filter coefficients

w=0:.01:pi;

h=freqz(hn,1,w);

plot(w/pi,abs(h),'-g');

xlabel('Normalised frequency');

ylabel('Magnitude');

title('LPF design using various windows')

hold off;

% FIR HPF USING WINDOWS

clc;

clear all;

wc=.5*pi;% cutoff frequency

N=25;

alpha=(N-1)/2;

eps=.001;

n=0:1:N-1;

hd=(sin(pi*(n-alpha+eps))-sin(wc*(n-alpha)))./(pi*(n-alpha+eps));



w=0:.01:pi;

h=freqz(hn,1,w);




hold on

wh=hamming(N); % rectangular window sequence


w=0:.01:pi;

h=freqz(hn,1,w);


hold on

wb=blackman(N); % rectangular window sequence


w=0:.01:pi;

h=freqz(hn,1,w);




title('HPF design using various windows')

hold off;

% FIR BPF USING WINDOWS

clc;

clear all;

wc1=.25*pi;wc2=.75*pi;% cutoff frequency

N=25;

alpha=(N-1)/2;

eps=.001;

n=0:1:N-1;

hd=(sin(wc2*(n-alpha+eps))-sin(wc1*(n-alpha)))./(pi*(n-alpha+eps));





w=0:.01:pi;

h=freqz(hn,1,w);


hold on

wh=hamming(N); % rectangular window sequence


w=0:.01:pi;

h=freqz(hn,1,w);


hold on

wb=blackman(N); % rectangular window sequence


w=0:.01:pi;

h=freqz(hn,1,w);




title('BPF design using various windows')

hold off;

% FIR Band reject Filter USING WINDOWS

clc;

clear all;

wc1=.25*pi;wc2=.75*pi;% cutoff frequency

N=25;



alpha=(N-1)/2;

eps=.001;

n=0:1:N-1;

hd=(sin(wc1*(n-alpha+eps))-sin(wc2*(n-alpha))+sin(pi*(n-alpha+eps)))./(pi*(n-alpha+eps));

wr=boxcar(N);%rectangular window sequence


w=0:.01:pi;

h=freqz(hn,1,w);


hold on

wh=hamming(N);%rectangular window sequence

hn=hd.*wh';%filter coefficients

w=0:.01:pi;

h=freqz(hn,1,w);


hold on

wb=blackman(N);


w=0:.01:pi;

h=freqz(hn,1,w);


xlabel('Normalised frequency'); ylabel('Magnitude');

title('BRF design using various windows')

hold off;

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