MATLAB: Filtering noise from an audio signal

fftfilterfrequencynoise frequency

Hi,

I have an audio signal, and I have two plots in the freq domain, amp vs freq and pow vs freq. Graphs attached.Can someone please tell me how do I find out which is the noise frequency and which is the sound frequency.

Code used for the plot:

Amp plot:

frequency_noise1 = fft(samples_noise1);

L = size(samples_noise1,1);

Fn = freqeuncyS_noise1/2;

FTy = frequency_noise1/L;

Fv = (linspace(0, 1, L/2)*Fn)/1000; %converting to KHz

Iv = 1:numel(Fv); % to match the vector sizes of X and Y

plot(Fv, abs(FTy(Iv,:)));

xlim([0 15]); %show x lim 0-5, 0-10, 0-15

ylim([0 0.01]);

title('Music plot Freq vs Amplitude')

set(gca, 'fontsize', 16);

xlabel('Frequency(KHz)');

ylabel('Amplitude(arb)');

Pow plot:

frequency_noise1 = fft(samples_noise1);

numberOf_samples = length(samples_noise1); % number of samples

f = (0:numberOf_samples-1)*(freqeuncyS_noise1/numberOf_samples); % frequency range

power = abs(frequency_noise1).^2/numberOf_samples; % power of the DFT

plot(f,power)

xlabel('Frequency')

ylabel('Power')

And also which filter should I chose to filter out my noise frequency

Best Answer

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hello again

I like simple solutions - see demo code below adapted to your case

I hope 200 dB attenuation can be considered as "complete washed out" !!

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 1024*4;    % 
NOVERLAP = round(0.75*NFFT);
w = hanning(NFFT);     % Hanning window / Use the HANN function to get a Hanning window which has the first and last zero-weighted samples.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% test data
Fs = 1000;
t = 0:1/Fs:10-1/Fs;
signal = cos(2*pi*50*t)+cos(2*pi*100*t);
 
%% notch filter section %%%%%%
% H(s) = (s^2 + 1) / (s^2 + s/Q + 1)
fc = 50;       % notch freq
wc = 2*pi*fc;
Q = 2;         % adjust Q factor for wider (low Q) / narrower (high Q) notch
                % at f = fc the filter has gain = 0
w0 = 2*pi*fc/Fs;
alpha = sin(w0)/(2*Q);
            b0 =   1;
            b1 =  -2*cos(w0);
            b2 =   1;
            a0 =   1 + alpha;
            a1 =  -2*cos(w0);
            a2 =   1 - alpha;
            
% analog notch (for info)
num1=[1/wc^2 0 1];
den1=[1/wc^2 1/(wc*Q) 1];
% digital notch (for info)
num1z=[b0 b1 b2];
den1z=[a0 a1 a2];
freq = linspace(fc-1,fc+1,200);
[g1,p1] = bode(num1,den1,2*pi*freq);
g1db = 20*log10(g1);
[gd1,pd1] = dbode(num1z,den1z,1/Fs,2*pi*freq);
gd1db = 20*log10(gd1);
figure(1);
plot(freq,g1db,'b',freq,gd1db,'+r');
title(' Notch: H(s) = (s^2 + 1) / (s^2 + s/Q + 1)');
legend('analog','digital');
xlabel('Fréquence (Hz)');
ylabel(' dB')
 
% now let's filter the signal 
signal_filtered = filtfilt(num1z,den1z,signal);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% display : averaged FFT spectrum before / after notch filter
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[sensor_spectrum, freq] = pwelch(signal,w,NOVERLAP,NFFT,Fs);
sensor_spectrum_dB = 20*log10(sensor_spectrum);% convert to dB scale (ref = 1)

[sensor_spectrum_filtered, freq] = pwelch(signal_filtered,w,NOVERLAP,NFFT,Fs);
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figure(2),semilogx(freq,sensor_spectrum_dB,'b',freq,sensor_spectrum_filtered_dB,'r');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
legend('before notch filter','after notch filter');
xlabel('Frequency (Hz)');ylabel(' dB')

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