DESIGN FIR LOWPASS FILTER WITH CUTOFF FREQUENCY 0.5*pi using RECTANGULAR WINDOW

clear all;
wcutoff=input('ENTER THE CUT OFF FREQUENCY in radians eg: 0.5*pi--->');
N=input('ENTER THE NUMBEROF SAMPLES eg: N=25--->');
alpha=(N-1)/2;
epso=.001;          %to prevent singularity when n=alphan=0:1:N-1;
hd=sin(wcutoff*(n-alpha+epso))./(pi*(n-alpha+epso));
                              %expression for FIR Lowpass filterwr=boxcar(N);       %expression for Rectangular window
hn=hd.*wr';            %wr'=transpose of wr
w=0:0.01:pi;
h=freqz(hn,1,w);    %MATLAB function for frequency response
xlabel('Normalised frequency \omega/\pi');
ylabel('Magnitude');
plot(w/pi,abs(h));  %to plot the graph

OUTPUT

ENTER THE CUT OFF FREQUENCY in radians eg: 0.5*pi--->0.5*pi
ENTER THE NUMBER OF SAMPLES eg: N=25--->31

PLOT

FIR LOWPASS FILTER USING RECTANGULAR WINDOW

MATLAB PROGRAM FOR IMPLEMENTING CHEBYSHEV LOW PASS FILTER

%chebyshev LPF
% specification
clear all;
alphap=input('pass band attenuation?=');
alphas=input('stop band attenuation in db?=');
wp=input('pass band frq in rad=');
ws=input('stop band freq in rad=');
% find cut-off freq and order of filter
[n,wn]=cheb1ord(wp/pi,ws/pi,alphap,alphas);
%system function above
[b,a]=cheby1(n,alphap,wn);
w=0:.01:pi;
[h,ph]=freqz(b,a,w);m=20*log(abs(h));
an=angle(h);
subplot(221);
plot(ph/pi,m);
grid;
ylabel('gain in db');
xlabel('nor fre');
subplot(212);
plot(ph/pi,an);
grid;
ylabel('phase in rad');
xlabel('norm freq');

OUTPUT WAVEFORM