Question

Design a LP FIR filter to meet the following specifications using the window method. Use a Blackman window.

Fs = 25 kHz

Fc = 5.0 kHz (3 dB down)

Attenuation = 80 dB at 7 kHz

Give all the relevant plots (impulse, frequency responses) and the performance of the final filter. Compare this filter to one designed using the optimal method .

Answer 1

Script:

clc;close all;clear all;

Fs=25000;

Fc=5000;wc=2*Fc/Fs;

width=2*pi*4000/Fs;

N=ceil(12*pi/width);

n=0:1:N;

wb=blackman(N+1)';

hh=fir1(N,wc);

%Impulse response

h=hh.*wb;

[H,f]=freqz(h,1,1024,Fs);

figure;

subplot(321)

stem(n,hh);grid;title('Ideal impulse response')

xlabel('n');ylabel('h(n)')

subplot(322)

stem(n,wb);grid;title('Blackman window')

xlabel('n');ylabel('wb(n)')

subplot(323)

stem(n,h);grid;title('desired impulse response')

xlabel('n');ylabel('hd(n)')

subplot(324)

plot(f,abs(H));grid;title('Freqeuncy response-Magntiude')

xlabel('f in Hz');ylabel('|H(f)|')

subplot(325)

plot(f,20*log10(abs(H)));grid;title('Freqeuncy response-Magntiude in db')

xlabel('f in Hz');ylabel('|H(f)|')

subplot(326)

plot(f,angle(H));grid;title('Freqeuncy response-Phase')

xlabel('f in Hz');ylabel('<H(f)>')

figure;% optimal FIR filter design

Rs=80;

[N,fo,ao,w] = firpmord([3000 7000],[1 0],[0.001 10^(-Rs/20)],Fs);

h= firpm(N,fo,ao,w);

freqz(h,1,1024,Fs)

Plots:

using blackman window:

Optimal FIR filter design