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.

(Please use MATLAB to give all the answers)

Answer 1

m=80; % The length of the Karnel%

n=0:1:m-1; %Defines Range of position value%

p=n-(m-1)/2; %Angle%

fc=5; %Define Cutoff frequency%

Z=sin(2*pi*fc*p)./(pi*p); %Define truncated Sinc function%

stem(n,Z);grid %To represent the discrete signal value & draw the grid lines%

title('Unit Sample Response of the sin function') %Define the title of the figure%

xlabel('n') %Define the label of on x axis%

ylabel('Z') %Define the label of on y axis%

figure; %To draw a figure%

[h,w]=freqz(Z); %get Frequency Response%

plot(w/pi,abs(h));grid

title('Frequency response of the sin function')

xlabel('Frequency')

ylabel('Amplitude')

figure;

s=2*pi*(n/(m-1));              %Angle%

w=0.54-0.46*cos(s); %Define blackman window function%

stem(n,w);grid

title('blackman Window')

xlabel('n')

ylabel('w')

figure;

t=Z.*w;   %Multiplication of blackman Window and sin function%

stem(n,t);grid

title('Multiplication of blackman Window and sin function')

xlabel('n')

ylabel('t')

figure;

[h,w]=freqz(t);

plot(w/pi,abs(h));grid

xlabel('Frequency')

ylabel('Magnitude')

title('Frequency response of the windowed sin function')

figure;grid

freqz(t)

title('Frequency Response of the windowed sin function in dB')