Question

MATLAB

Filter Design using the Parks-McClellan Algorithm Using the Parks-McClellan (PMC) algorithm, design filters with the following specifications: A. Filterlspecifications: Type: lowpass filter Cutoff frequencies: o 0.1t and o0.3 Tolerances: PB 1 dB; SB 40 dB B. Filter 2 specifications: Type: highpass filter Cutoff frequencies: o 0.9 and o0.77 Tolerances: PB 1 dB; SB 40 dB stl Respond to the following questions, a. What is the order of the filter in each case? b. Design the FIR filter using the Kaiser window method for the above specifications and find the order of the filter

Answer 1

Bleow is the matlab code. The filter order is given in image title.

close all,
clear all,
clc,

Fs = 2*pi; % Sampling frequency

rp = 1; % Passband ripple
rs = 40; % Stopband ripple
f = [0.1*pi 0.3*pi]; % Cutoff frequencies
a = [1 0]; % Desired amplitudes Low Pass Filter

figure,
dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)];
[n,fo,ao,w] = firpmord(f,a,dev,Fs);
b = firpm(n,fo,ao,w);
freqz(b,1,1024,Fs);
str=strcat('Lowpass Filter Designed to Specifications at Order = ',num2str(n)); title(str);

rp = 1; % Passband ripple
rs = 40; % Stopband ripple
f = [0.7*pi 0.9*pi]; % Cutoff frequencies
a = [0 1]; % Desired amplitudes High pass Filter
figure,
dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)];
[n,fo,ao,w] = firpmord(f,a,dev,Fs);
b = firpm(n,fo,ao,w);
freqz(b,1,1024,Fs);
str=strcat('Highpass Filter Designed to Specifications at Order = ',num2str(n)); title(str);

rp = 1; % Passband ripple
rs = 40; % Stopband ripple
f = [0.1*pi 0.3*pi]; % Cutoff frequencies
a = [1 0]; % Desired amplitudes Low Pass Filter
figure,
dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)];
[n,Wn,beta,ftype] = kaiserord(f,a,dev,Fs);
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');
freqz(hh)
str=strcat('Lowpass Filter Designed using Kaiser Window to Specifications at Order = ',num2str(n)); title(str);

rp = 1; % Passband ripple
rs = 40; % Stopband ripple
f = [0.7*pi 0.9*pi]; % Cutoff frequencies
a = [0 1]; % Desired amplitudes High pass Filter
figure,
dev = [(10^(rp/20)-1)/(10^(rp/20)+1) 10^(-rs/20)];
[n,Wn,beta,ftype] = kaiserord(f,a,dev,Fs);
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');
freqz(hh)
str=strcat('Highpass Filter Designed using Kaiser Window to Specifications at Order = ',num2str(n)); title(str);

Highpass Filter Designed to Specifications at Order 14 60 25 30 1.5 0.5 Frequency (Hz) 300 200 100 2.5 15 0.5 200 Frequency (Hz) en aseu ....Gv Magnitude (dE)

Lowpass Filter Designed to Specifications at Order 14 20 0 20 A0 60 80 25 100 15 05 Frequency (Hz) 100 200 300 2.5 1.5 05 400 Frequency (Hz) coeni n) aseu- Magnitude (dB)

Highpass Filter Designed using Kaiser Window to Specifications at Order 24 20 20 40 60 80 09 08 n 7 0.5 100 04 0.3 0.2 0.1 Normalized Frequency (xn rad/sample) 300 200 10 100 200 200 09 0.8 n z 0 03 0.4 0.2 -400 01 Normalized Frequency (x rad/sample) Magnitude (dB) seni anl aseu-

amalized Frequency (xTrad/samgle (gp) epnuubew (seeep 8seud