DSP

                                                                           

Design a low pass chebyshev filter with specifications

pass band edge frequency=250Hz

stop band edge frequency=375Hz

sampling frequency=1000Hz

stopband attenuation=13.98dB

pass band gain=3.01dB

use bilinear transformation

PROGRAM:

clc;

clear all;

close all;

ap=3.01

as=13.98

fp=250

fs=375

Fs=1000

T=1/Fs

wp=2*pi*fp/Fs

ws=2*pi*fs/Fs

ohmp=(2/T)*tan(wp/2)

ohms=(2/T)*tan(ws/2)

%% To find the order N

s1=10^(0.1*as)-1

s2=10^(0.1*ap)-1

s3=ohms/ohmp

N=acosh(sqrt(s1/s2))/acosh(s3)

%% to make the order upper side

N=ceil(N)

%% To find epslm value(e)

e=sqrt(s2)

%% To find the value of Bita(b)

b=(sqrt(1+(e*e))+1/e)^(1/N)

%% to find the r

s4=b*b-1

r=ohmp*(s4)/(2*b)

%% To find the R

s5=(b*b)+1

R=ohmp*(s5)/(2*b)

%% To find the Thita Qk

Q=0

for k=1:N

Q(k)=(pi/2)+(2*(k-1)+1)*pi/(2*N)

s(k)=r*cos(Q(k))+j*R*sin(Q(k))

end

%% To find the gain(K) Order=2 i.e (Even)

q=poly(s)

b0=q(N+1)

r1=rem(N,2)

if(r1==0)

K=b0/(sqrt(1+e^2))

else

K=b0

end

K=abs(K)

freqs(K,q,100000)