Question

matlab code as well please.

7. (100) Design a bandpass FIR filter with the following Spec: (a) Lower cut off frequency: 1250Hz, (b) lower transition width: 1500Hz, (c) upper cutoff frequency: 2850 Hz, (d) upper transition width: 1300 Hz, (e) stop band attenuation: 60dB, (f) passband ripple 0.02 dB, and (g) sampling frequency: 8000Hz. Your answer needs to include (i) normalized frequencies, (ii) Window type, (iii) order of the filter and their numerical values computed by matlab command firwd(), and (iv) plot the frequency and phase response.

Answer 1

window type

For the attenuation of 60 db,either blackman or hamming window should be selected. But the mainlobe width provided by the blackman window is 8pi/N when compared with the main lobe width of the HAMMING window(4pi/N).

Order

Main lobe width of Hamming window= 8 pi/N ---(1)

Minimum transition width of the filter(1500,1300)=1300Hz---(2)

By comparing 1 and 2,

8 X pi/N = 2*pi*1300/sampling frequency

8 Xpi/N= 2*pi*15=300/8000

N=8/0.325 =24.6

M>=N

Hence M=25

MATLAB script:

clc;close all;clear all;

M=25;%order

fc1=1250;fc2=2850;%cut off frequencies

Fs=8000;WL=2*fc1/Fs;WH=2*fc2/Fs;

Wtype=hamming(M)';

Ftype='bandpass';

B=firwd(M-1,Ftype,WL,WH,Wtype);

w=0:pi/1000:pi;

H=freqz(B,1,w);

n=0:1:M-1;

figure;

subplot(311)

stem(n,B)

xlabel('n')

ylabel('h(n)')

title('impulse response')

subplot(312)

plot(w/pi,abs(H));xlabel('w X pi')

ylabel('|H(exp(jw)|')

title('Magnitude response')

subplot(313)

plot(w/pi,angle(H));xlabel('w X pi')

ylabel('<H(exp(jw)>')

title('Phase response')

B_Impulse response coefficients:

Columns 1 through 18

0.0003 0.0001 0.0000 0.0007 -0.0069 -0.0041 0.0176 -0.0000 0.0545 0.0177 -0.2644 -0.0142 0.3980 -0.0142 -0.2644 0.0177 0.0545 -0.0000

Columns 19 through 25

0.0176 -0.0041 -0.0069 0.0007 0.0000 0.0001 0.0003

Function script:

function B=firwd(M,Ftype,WL,WH,Wtype)

Wc=[WL WH]

h=fir1(M,Wc,Ftype)

B=h.*(Wtype)

end