Digital Signal Processing Filters

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

[y,Fs] = audioread("mySpeech.wav");

[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

Answer 1

[Paul]

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]

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))