# Digital Signal Processing Filters

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Mustafa Kemal Tasci on 25 Dec 2022
Hello, I am new to Matlab. I have problems could you help me with these ? I recorded my speech that said "Hello Friend" in a noisy environment. I want to design a filter that reduces noise and uses group delay to observe "Friend Hello" at the output. I designed an arbitrary filter to observe what is happening I have an issue also in the graph of frequency axises are wrong filter parameters and they are not match
Here are my codes:
clc
close all
clear
[N,P] = size(y);
ts = 1/Fs; % ts is the sampling period
tmax= (N-1)*ts; % tmax is the maxmimum period
t = 0:ts:tmax; % Defines a vector t that starts from 0 upto tmax increaments by the amount of sampling period
f = 0:pi/N:pi-pi/N; % For plotting the frequency spectrum
figure("Name","Time Domain Analysis")
subplot(2,1,1)
plot(t,y)
title("Unfiltered Signal in Time"); xlim([0, tmax]); xlabel("Time (sec)"); ylabel("Magnitude")
%%sound(y, Fs)
z = filter(Filter,y);
subplot(2,1,2)
plot(t,z)
title("Filtered Signal in Time"); xlim([0, tmax]); xlabel("Time (sec)"); ylabel("Magnitude")
sound(z, Fs)
Y = fftshift(fft(y));
figure("Name", "Frequency Domain Analysis")
subplot(2,1,1);
plot(f/pi,20*log10(abs(Y)))
title("Unfiltered Signal in Frequency"); xlabel("Frequency (Hz)"); ylabel("Magnitude (dB)")
Z = fftshift(fft(z))
subplot(2,1,2);
plot(f/pi,20*log10(abs(Z)))
title("Filtered Signal in Frequency"); xlabel("Frequency (Hz)"); ylabel("Magnitude (dB)")
fvtool(Filter)
freqz(Filter)
title("Magnitude Response")
subplot(2,1,2)
plot("""");
title("Phase Response")
function Hd = Filter
%FILTER Returns a discrete-time filter object.
% MATLAB Code
% Generated by MATLAB(R) 9.11 and Signal Processing Toolbox 8.7.
% Generated on: 25-Dec-2022 22:16:37
% Equiripple Bandpass filter designed using the FIRPM function.
% All frequency values are normalized to 1.
Fstop1 = 0.09; % First Stopband Frequency
Fpass1 = 0.12; % First Passband Frequency
Fpass2 = 0.25; % Second Passband Frequency
Fstop2 = 0.3; % Second Stopband Frequency
Dstop1 = 0.001; % First Stopband Attenuation
Dpass = 0.057501127785; % Passband Ripple
Dstop2 = 0.0001; % Second Stopband Attenuation
dens = 20; % Density Factor
% Calculate the order from the parameters using FIRPMORD.
[N, Fo, Ao, W] = firpmord([Fstop1 Fpass1 Fpass2 Fstop2], [0 1 0], ...
[Dstop1 Dpass Dstop2]);
% Calculate the coefficients using the FIRPM function.
b = firpm(N, Fo, Ao, W, {dens});
Hd = dfilt.dffir(b);
% [EOF]
end

Paul on 25 Dec 2022
Edited: Paul on 25 Dec 2022
Hi Mustafa,
Not checking all of the code in detail, but I did notice that the fft plots don't look correct. They should be:
f = ceil(linspace(-N/2,N/2-1,N))/N*Fs; % Hz
Y = fftshift(fft(y));
figure("Name", "Frequency Domain Analysis")
subplot(2,1,1);
%plot(f/pi,20*log10(abs(Y)))
plot(f,20*log10(abs(Y)))
title("Unfiltered Signal in Frequency"); xlabel("Frequency (Hz)"); ylabel("Magnitude (dB)")
Z = fftshift(fft(z))
subplot(2,1,2);
%plot(f/pi,20*log10(abs(Z)))
plot(f,20*log10(abs(Z)))
title("Filtered Signal in Frequency"); xlabel("Frequency (Hz)"); ylabel("Magnitude (dB)")
Also, can this statement be clarified: "uses group delay to observe "Friend Hello" at the output." I'm not sure how group delay relates to swapping two portions of the signal.
Mustafa Kemal Tasci on 26 Dec 2022
Thank you Paul. I want to design a filter that removes the noise and delays the "Hello" part but I don't know. In theory, if I add a group delay to the frequency range where "Hello" is located, "Hello" will be delayed in time.
This is the my professor's example code :
clear all
close all
clc
%%% signal generation %%%
f1=5; %frequency1
f2=12; %frequency2
fs=100; %sampling frequency
ts=1/fs; %sampling interval
t=1:ts:5; %speech duration in s
x=[zeros(400,1); sin(t*2*pi*f1)'; zeros(200,1); sin(t*2*pi*f2)'; zeros(3000,1)];
lx=length(x);
y=x+0.1*randn(lx,1); y=y/max(y);
figure(1), plot(y)
%%% signal analysis %%%
% N=2^15;
N=lx;
y_f=fft(y,N);
y_f_a=abs(y_f);
eks=fs*(0:N/2)/N;
figure(2), plot(eks,20*log10(y_f_a(1:N/2+1).^2))
%%% filter design %%%
b1=fir1(50,[10 15]/(fs/2),'bandpass');
[H1,w1] = freqz(b1,1,N,'whole');
H = (H1(1:N/2)); w = (w1(1:N/2));
mag = abs(H);
db = 20*log10((mag)/max(mag));
pha = angle(H);
grd = grpdelay(b1,1,w);
figure(3), plot(w/pi,db);
figure(4), plot(w/pi,grd);
yfil1=filter(b1,1,y);
b2=fir1(3000,[3 8]/(fs/2),'bandpass');
yfil2=filter(b2,1,y);
yfil=yfil1+yfil2;
figure(5), plot(yfil)
yfil_f=fft(yfil,N);
yfil_f_a=abs(yfil_f);
figure(6),
plot(eks,20*log10(yfil_f_a(1:N/2+1).^2))

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