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I need to bandpass filter the white noise signal of 2 sec lenght and my teacher wants me to use fft() to go from time domain to frequency domain, where I can just give value of 0 to frequencies of non interest. And then using ifft() to go back to time domain. The problem is: when I convert back to time domain the amplitude of the last 0.8 sec of the signal is near 0. Someone can look at my code and finde a problem, please?

%% Generate white noise

Fs = 40000; % Sampling frequency

F = 1000; % center frequency

t = 0:1/Fs:2; % Time vector

L = length(t); % Signal length

X=wgn(L,1,0); % White noise at 0 dB

figure(1)

plot(t,X)

title('White noise')

xlabel('Time (sec)')

ylabel('X(t)')

%% Cenvert from time domain to frequensy domain

n = 2^nextpow2(L);

Y = fft(X,n);

f = Fs*(0:n-1)/n;

P = abs(Y/n);

figure(2)

plot(f,P)

title('White noise in Frequency Domain')

xlabel('Frequency (Hz)')

ylabel('|P(f)|')

%% Bandpass filtering 1 ocatve centered at 1 kHz

N=length(Y);

bw_low=round(N*F/(Fs*sqrt(2)));

bw_high=round(N*F*sqrt(2)/Fs);

bw_low_s=round((Fs-2*F+F/sqrt(2))*N/Fs);

bw_high_s=round((Fs-2*F+F*sqrt(2))*N/Fs);

Y(1:bw_low-1)=0;

Y(bw_high+1:bw_low_s-1)=0;

Y(bw_high_s+1:end)=0;

P_BP = abs(Y/n);

figure(3)

plot(f,P_BP)

title('Bandpass White noise in Frequency Domain')

xlabel('Frequency (Hz)')

ylabel('|P(f)|')

%% Convert from frequency domain to time domain

X_1 = ifft(Y,L);

figure(4)

plot(t,X_1);

title('1 octave White noise centered at 1 kHz')

xlabel('Time (sec)')

ylabel('X(t)')

%%

Dimitris Kalogiros
on 27 Sep 2019

Hi Anna.

Pay attention to these lines of your code:

n = 2^nextpow2(L);

Y = fft(X,n);

Because n>L, matlab adds some zeros at the end of signal X , in order to increase its length up to n. These are the zeros that you obzerve at the last figure;

I 'm giving you a "somewhat corrected" version of your code:

%% Generate white noise

Fs = 40000; % Sampling frequency

F = 1000; % center frequency

t = 0:1/Fs:2; % Time vector

L = length(t); % Signal length

X=wgn(L,1,0); % White noise at 0 dB

figure(1)

plot(t,X)

title('White noise')

xlabel('Time (sec)')

ylabel('X(t)')

%% Cenvert from time domain to frequensy domain

n = 2^nextpow2(L);

Y = fft(X,n);

f = Fs*(0:n-1)/n;

P = abs(Y/n);

figure(2)

plot(f,P)

title('White noise in Frequency Domain')

xlabel('Frequency (Hz)')

ylabel('|P(f)|')

%% Bandpass filtering 1 ocatve centered at 1 kHz

N=length(Y);

bw_low=round(N*F/(Fs*sqrt(2)));

bw_high=round(N*F*sqrt(2)/Fs);

bw_low_s=round((Fs-2*F+F/sqrt(2))*N/Fs);

bw_high_s=round((Fs-2*F+F*sqrt(2))*N/Fs);

Y(1:bw_low-1)=0;

Y(bw_high+1:bw_low_s-1)=0;

Y(bw_high_s+1:end)=0;

P_BP = abs(Y/n);

figure(3)

plot(f,P_BP)

title('Bandpass White noise in Frequency Domain')

xlabel('Frequency (Hz)')

ylabel('|P(f)|')

%% Convert from frequency domain to time domain

%X_1 = ifft(Y,L);

X_1 = ifft(Y,n);

X_1=X_1(1:length(X)); %remove n-L zeros.

figure(4)

%plot(t,X_1);

plot(t,real(X_1));

title('1 octave White noise centered at 1 kHz')

xlabel('Time (sec)')

ylabel('X(t)')

Tip: You used fft of length n, to trasform from time to frequency domain. You should use ifft of the same length (e.g. n ) to go back , from frequency to time domain.

Dimitris Kalogiros
on 27 Sep 2019

Well... In my laptop, everything seems OK. I can hear X , using sound(X, Fs), and it is totaly a white noise signal and I can listen X_1 , using sound (real(X_1), Fs), and the differences from X are evident.

I think that the error you are getting has to do with your sound card and not with the matlab code.

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