Question

please answer all the question and print matlab code

You need to design bandpass filter with lower cutoff freq. of 1000Hz and upper cutoff freq. of 3000Hz. Sampling freq. 10000Hz. Plot the freq. response in DB .Use MATLAB as needed

a) FIR with Hamming window at least 7 taps

b) IIR using Bilinear Transformation method not more than 2end order.

c) Compare the frequency response “freqz” plots and which method you recommend and why? 2 graphs on this part.

d) Determine the output of the filters for sinusoidal input with frequency 500Hz and 2000Hz for both filters. You may use the “filter” command. 4 graphs on this part. This will give time domain response.

Answer 1

The specifications are as follows:

lower cutoff freq = f1 = 1000 Hz

upper cutoff freq = f2 = 3000 Hz

Sampling freq = fs = 10000 Hz

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MATLAB code for all the four subsections is written below,

---------- START OF MATLAB CODE ---------------------

%------------------------------------------
% FIR with Hamming window
%------------------------------------------
% Lower cutoff freq
f1 = 1000; % f1 = 1000 Hz
% Upper cutoff freq
f2 = 3000; % f2 = 3000 Hz
% Sampling freq
fs = 10000; % fs = 10000 Hz
% Normalized lower and upper cutoff frequencies
w1 = f1/fs;
w2 = f2/fs;
% Creation of FIR filter with Hamming window
N = 7; % Atleast 7 taps of Hamming window
bf = fir1(N,[w1,w2],'bandpass','hamming');
% Frequency response of FIR Hamming window
figure,freqz(bf,1,500,fs)
grid on;

%---------------------------------------
% IIR with bilinear transformation
%---------------------------------------
% Order of the filter
n = 2;
% Cut-off frequencies in radians per second
w1 = 2*pi*f1;
w2 = 2*pi*f2;
% Butterworth filter in 's'
[num,den] = butter(n, [w1, w2], 's');
% Applying bilinear transform
[bi,ai] = bilinear(num, den, 1/fs);
% Frequency response of IIR filter
figure,freqz(bi,ai,500,fs);
grid on;

%----------------------------------
% Time domain analysis for 500 Hz
%----------------------------------
% Frequency
ft = 500; % 500Hz
% Time for 10 cycles
T = 10/ft;
% Time sequence to construct signal for time domain analysis
t = 0:1/fs:T;
% Generation of signal of 500 Hz
x = sin(2*pi*ft*t);
% Filter signal using FIR filter
xf = filter(bf,1,x);
% Plotting the signal
figure,subplot(2,1,1),plot(t,x),grid on,xlabel('Time (s)'),ylabel('Amplitude (v)'),hold on
subplot(2,1,2),plot(t,xf),xlabel('Time (s)'),ylabel('Amplitude (v)'),grid on
% Filter signal using IIR filter
xi = filter(bi,ai,x);
% Plotting the signal
figure,subplot(2,1,1),plot(t,x),grid on,xlabel('Time (s)'),ylabel('Amplitude (v)'),hold on
subplot(2,1,2),plot(t,xi),xlabel('Time (s)'),ylabel('Amplitude (v)'),grid on

%----------------------------------
% Time domain analysis for 2000 Hz
%----------------------------------
% Frequency
ft = 2000; % 500Hz
% Time for 10 cycles
T = 10/ft;
% Time sequence to construct signal for time domain analysis
t = 0:1/fs:T;
% Generation of signal of 2000 Hz
x = sin(2*pi*ft*t);
% Filter signal using FIR filter
xf = filter(bf,1,x);
% Plotting the signal
figure,subplot(2,1,1),plot(t,x),grid on,xlabel('Time (s)'),ylabel('Amplitude (v)'),hold on
subplot(2,1,2),plot(t,xf),xlabel('Time (s)'),ylabel('Amplitude (v)'),grid on
% Filter signal using IIR filter
xi = filter(bi,ai,x);
% Plotting the signal
figure,subplot(2,1,1),plot(t,x),grid on,xlabel('Time (s)'),ylabel('Amplitude (v)'),hold on
subplot(2,1,2),plot(t,xi),xlabel('Time (s)'),ylabel('Amplitude (v)'),grid on

---------- END OF MATLAB CODE -----------------------

Each command line is accompanied with a comment. Save the code in a single MATLAB file as 'analyze.m' and run the command 'analyze' in MATLAB command window. All the figures are generated as required in the problems.

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a) FIR Hamming window frequency response is shown below,

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b) IIR bilinear transformation with second order butterworth filter frequency response is shown below,

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c) The above frequency response plots were generated using 'freqz' command. If we observe the frequency response plots and especially the phase response. The phase response is linearly increasing for FIR filter, where as IIR filter has varying phase for different frequencies. Phase response is important to preserve the shape of the signal. If the phase is linearly varying then the shape of the signal doesn't distort. Hence, FIR filter is butter than the IIR filter.

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d) (1) Time domain analysis of 500 Hz using FIR filter.

The time domain plot is shown below,

(2) Time domain analysis of 500 Hz using IIR filter.

The time domain plot is shown below,

(3) Time domain analysis of 2000 Hz using FIR filter.

The time domain plot is shown below,

(4) Time domain analysis of 2000 Hz using IIR filter.

The time domain plot is shown below,

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Note: For 2000 Hz signal, there are four distinct segments in the input generated signal.

We can see FIR filtered signal has similar four distinct segments. But, we cannot see all the four segments in IIR filtered signal. So, the shape of the signal is distorted when filtered with IIR filter.

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