Why does the psd of my filtered signal perfectly overlap my raw signal's one?

I have been given an eeg signal that has already been filtered passband [1Hz 30Hz] and resampled from 128Hz to 64Hz.

I obtained its psd using pwelch and, because there was still quite the activity after 30Hz, I tried to filter it lowpass with a cutoff frequency of 30Hz. I tried with both cheby2 and butter, but the psd of the filtered signal is a perfect match with the previous one.

% Butter

fny = fc/2;

ft_l = 30/fny;

order = 5;

[b_l, a_l] = butter(order,ft_l,"low");

freqz(b_l,a_l,NFFT,fc)

% Cheby2

Wp = 30/fny;

Ws = 35/fny;

Rp = 1;

Rs = 60;

[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);

[z,p,k] = cheby2(n,Rs,Ws);

[sos,g] = zp2sos(z,p,k);

figure, freqz(sos, 2^16, fc)

Answer 1

[Mathieu NOE]

hello

see code below, the effect of the low pass filter is clearly to be seen on the psd plot

now I wonder whatkind of "activity" you can see above 30 Hz for a signal sampled at 64 Hz (??)

to avoid such strange sitation, the demo below has fc = 100 Hz (NB I would prefer "fs" for the sampling rate , as "fc" is usualy something that is related to a cuting / corner frequency

% dummy signal 
fc = 100; % sampling rate 
x = randn(1000,1);

% Butter 
fny = fc/2; 
ft_l = 30/fny;    
order = 5;
[b_l, a_l] = butter(order,ft_l,"low");
NFFT = 128;
freqz(b_l,a_l,NFFT,fc)

y = filter(b_l, a_l,x); % filter the signal 

% psd 
p1 = pwelch(x);
p2 = pwelch(y);
f = linspace(0,fny,numel(p1));
figure
semilogy(f,p1,'b',f,p2,'r')

[Mathieu NOE]

hello again

problem solved ?

[Matteo Agresti]

Yes, thank you very much.