Question

(a) Does it have to be this way? Briefly explain, is it possible to have an online FIR filter without a window function? (b) Low-Pass Filter Consider the ideal impulse response of a low pass filter (of cut-off frequency given by hLP [n] = 0, sinc (odn-부) for a filter size N. Thus, hw InhnwHAM Now consider the case where N-100 and oc 0.3004. Determine hw, In] using the formula above. Then generate a FIR filter in Matlab (or equivalent) using the command firl. Briefly explain, are these filters the same? Using the plotting tool freqz to see the difference of these filters.

Please do both questions! thank you very much!

Answer 1

a)Yes .This is possible with Parks-McClellan optimal FIR filter design using FIRPM command and Least-squares linear-phase FIR filter design using firls.

EX: Uisng FIRPM

f = [0 0.5 0.6 1];

a = [ 1 1 0 0];

b = firpm(17,f,a);

freqz(b,1,512);

20 0 ︶-20 g 40 60 -80 -100 0.2 0.4 0.6 0.8 Normalized Frequency (×π rad/sample) 0 -500 -1000 a) -1500 -2000 2500 0.2 0.6 0.8 0.4 Normalized Frequency (x π rad/sample)

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b)Using HAmming window:

(i)

MATLAB:

clc;clear all;close all;

N=100;wc=0.3004;
n=0:1:N-1
hLP=wc*(sinc(wc.*(n-((N-1)/2))))
WHAM=hamming(N)'
hWLP=hLP.*WHAM

%Magnitude response
w=0:0.01*pi:pi
[H,w]=freqz(hWLP,[1],w)

figure(1)
subplot(221)
stem(n,WHAM,'r')
title('Hamming window ')
xlabel('n')
ylabel('wh(n)')

subplot(222)
stem(n,hWLP,'m')
title('Impulse response h(n)')
xlabel('n')
ylabel('h(n)')

subplot(223)
plot(w/pi,abs(H),'b')
title('Magnitude response ')
xlabel('w/pi')
ylabel('|H(exp(jw)|')

subplot(224)
plot(w/pi,angle(H),'b')
title('Phase response ')
xlabel('w/pi')
ylabel('<H(exp(jw)>')

figure(2)
freqz(hWLP,[1])

Hamming window Impulse response h(n) 0.3 0.8 0.6 30.4 0.2 S 0.1 0.2 0.1 40 60 80 20 40 60 20 80 100 100 Magnitude response Phase response 4 2 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 w/pi 0.2 0.4 0.6 0.8

100 Ф-100 -200 -300 400 0.6 0.8 0.2 0.4 Normalized Frequency (×π rad/sample) 500 3 -1000 -1500 g -2000 Q -2500 -3000 3500 0.6 0.8 0.2 0.4 Normalized Frequency (xt rad/sample)

ii)MATLAB:

N=100;wc=0.3004;
h=fir1(N,wc)
freqz(h,1)

50 2-50 2 -100 150 0.6 0.8 0.2 0.4 Normalized Frequency (xt rad/sample) 500 3 -1000 -1500 g -2000 Q -2500 -3000 3500 0.6 0.8 0.2 0.4 Normalized Frequency (×π rad/sample)

The response produced by FIR1 command and the response produced by using Hamming window without using FIR1 command- both are same why because the the command FIR1 uses hamming window for its windowing process.