Remez exchange algorithm

Matlab program for Remez exchange algorithm.

[n,fo,ao,w] = firpmord(f,a,dev,fs). Finds the approximate order, normalized frequency band edges, frequency band amplitudes, and weights.

b = firpm(n,f,a,w) returns row vector b containing the n+1 coefficients of the order n FIR filter whose frequency-amplitude characteristics match those given by vectors f and a.

Matlab code

clc; clear all; close all;

rp=input('Enter the Passband ripple (In db) = '); 

rs=input('Enter the Stopband attenuation (In db) = '); 

fpc=input('Enter the Passband corner frequency (In Hz) = '); 

fsc=input('Enter the Stopband corner frequency (In Hz) = '); 

fs=input('Enter the Sampling frequency (In Hz) = ');

f = [fpc fsc]; % f is a vector of frequency band edges

a = [1 0]; % Desired amplitudes on the bands defined by f.

dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)]; % Compute deviations by rp & rs

[n,fo,ao,w] = firpmord(f,a,dev,fs); b = firpm(n,fo,ao,w);

[h,fn] = freqz(b,1,1024,fs);% Denominator polynomials a = 1

subplot(3,1,1);

plot(fo,ao,'r');

hold on;

plot(fn/(fs/2),abs(h)); 

legend('Ideal','firpm Design')

title('Comparison b/w Ideal & firpm Design'); 

ylabel('Magnitude -->');

xlabel('Normalized Frequency ( x pi rad/sample)-->') 

grid on;

subplot(3,1,2); 

plot(fn/(fs/2),20*log10(abs(h))); 

title('Magnitude Response of Lowpass Filter'); 

ylabel('Gain in dB -->');

xlabel('Normalized Frequency ( x pi rad/sample)-->') 

grid on;

subplot(3,1,3);
plot(fn/(fs/2),angle(h));

title('Phase Response of Lowpass Filter'); 

xlabel('Normalized Frequency ( x pi rad/sample)-->'); 

ylabel('Phase in radians -->');

grid on;

Command window

Enter the Passband ripple (In db) = 1

Enter the Stopband attenuation (In db) = 30

Enter the Passband corner frequency (In Hz) = 400

Enter the Stopband corner frequency (In Hz) = 600

Enter the Sampling frequency (In Hz) = 2000

Figure window