Question

7.29. Design a 41-tap bandpass FIR filter with lower and upper cutoff frequencies of 2,500 Hz and 3,000 Hz, respectively, using the following window functions. Assume a sampling frequency of 8,000 Hz.

a. Hanning window function

b. Blackman window function.

List the FIR filter coefficients and plot the frequency responses for each design.

7.30 Design a 41-tap band reject FIR filter with cutoff frequencies of 2,500 Hz and 3,000 Hz, respectively, using the Hamming window function. Assume a sampling frequency of 8,000 Hz. List the FIR filter coefficients and plot the frequency responses.

Answer 1

1)

clc;close all;clear all;
N=41
fc1=2500
fc2=3000
fs=8000
wc=[2*fc1/fs 2*fc2/fs ]
hd=fir1(N-1,wc,'pass')
wh=hanning(N)'%Hanning window
h=hd.*wh
figure;
%frequency response
freqz(h,1,1024,fs)

Command window:(FIR filter coefficients)

>> h
h =

Columns 1 through 10:

-0.00000 0.00001 -0.00002 -0.00003 0.00000 0.00017 0.00036 -0.00256 0.00405 0.00165

Columns 11 through 20:

-0.01553 0.02228 -0.00094 -0.04266 0.06294 -0.01762 -0.06953 0.11155 -0.04837 -0.07278

Columns 21 through 30:

0.13403 -0.07278 -0.04837 0.11155 -0.06953 -0.01762 0.06294 -0.04266 -0.00094 0.02228

Columns 31 through 40:

-0.01553 0.00165 0.00405 -0.00256 0.00036 0.00017 0.00000 -0.00003 -0.00002 0.00001

Column 41:

-0.00000

2)

clc;close all;clear all;
N=41
fc1=2500
fc2=3000
fs=8000
wc=[2*fc1/fs 2*fc2/fs ]
hd=fir1(N-1,wc,'pass')
wh=blackman(N)'%Blackman window
h=hd.*wh
figure;
%frequency response
freqz(h,1,1024,fs)

Command window:

>> h
h =

Columns 1 through 10:

0.00000 0.00000 -0.00001 -0.00001 0.00000 0.00008 0.00017 -0.00137 0.00235 0.00104

Columns 11 through 20:

-0.01056 0.01627 -0.00073 -0.03521 0.05464 -0.01596 -0.06528 0.10766 -0.04761 -0.07249

Columns 21 through 30:

0.13403 -0.07249 -0.04761 0.10766 -0.06528 -0.01596 0.05464 -0.03521 -0.00073 0.01627

Columns 31 through 40:

-0.01056 0.00104 0.00235 -0.00137 0.00017 0.00008 0.00000 -0.00001 -0.00001 0.00000

Column 41:

0.00000

Plot:

3)

clc;close all;clear all;
N=41
fc1=2500
fc2=3000
fs=8000
wc=[2*fc1/fs 2*fc2/fs ]
hd=fir1(N-1,wc,'stop')
wh=hamming(N)'%Blackman window
h=hd.*wh
figure;
%frequency response
freqz(h,1,1024,fs)

Command window:

>> h
h =

Columns 1 through 10:

0.00010 -0.00014 0.00006 0.00006 0.00000 -0.00023 -0.00043 0.00290 -0.00435 -0.00171

Columns 11 through 20:

0.01563 -0.02198 0.00091 0.04096 -0.05989 0.01664 0.06535 -0.10445 0.04517 0.06787

Columns 21 through 30:

0.87448 0.06787 0.04517 -0.10445 0.06535 0.01664 -0.05989 0.04096 0.00091 -0.02198

Columns 31 through 40:

0.01563 -0.00171 -0.00435 0.00290 -0.00043 -0.00023 0.00000 0.00006 0.00006 -0.00014

Column 41:

0.00010