MATLAB: How to filter and FFT raw data

digital signal processingFilter Design ToolboxfilteringSignal Processing Toolbox

Can someone help me with the matlab code:

I have a raw data (attached) from acoustic sensor. I want to filter the signal and carry out fft then plot the graph.

Best Answer

I am not certain what you want to do.

One approach:

D = load('exp 8b.txt');
t = D(:,1);
s = D(:,2);
figure
plot(t, s)
grid
title('Original Signal')
xlabel('Time')
ylabel('Amplitude')
sm = mean(s);
L = size(D,1);
Ts = mean(diff(t));
Fs = 1/Ts;
Fn = Fs/2;
FTs = fft(s-sm)/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn;
Iv = 1:numel(Fv);
figure
plot(Fv, abs(FTs(Iv))*2)
grid
title('Original Signal')
xlabel('Frequency')
ylabel('Amplitude')
sdn = wdenoise(s);                                  % Denoise (Wavelet Toolbox)
figure
plot(t, sdn)
grid
title('Denoised Signal')
xlabel('Time')
ylabel('Amplitude')
Wp = [859 862]/Fn;                                  % Passband Normalised
Ws = [855 865]/Fn;                                  % Stopband Normalised
Rp =  1;                                            % Passband Ripple (Irrelevant in Butterworth)
Rs = 50;                                            % Stopband Attenuation
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                     % Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp);                        % Zero-Pole-Gain 
[sos,g] = zp2sos(z,p,k);                            % Second-Order Section For Stability
figure
freqz(sos, 2^16, Fs)                                % Filter Bode Plot
s_filt = filtfilt(sos, g, s);                       % Filter Signal
figure
plot(t, s_filt)
grid
title('Filtered Signal')
xlabel('Time')
ylabel('Amplitude')
s_filt = filtfilt(sos, g, sdn);                       % Filter Denoised Signal
figure
plot(t, s_filt)
grid
title('Filtered Denoised Signal')
xlabel('Time')
ylabel('Amplitude')

Your signal has significant broadband noise, and a wavelet denoising step is the only way to deal with that. See the documentation for wdenoise (R2017b and later releases) for details on the function.

There appears to be a frequency peak at about 861 Hz, and the bandpass filter here selectively (and efficiently) filters the region from 859 Hz to 862 Hz.

Expertiment to get the result you want.

Related Solutions

MATLAB: Designing IIR band-pass filter for signal with white noise

The filter is unstable, and that is the problem. You can see this if you look at the coefficients returned by cheby1 and analyse it first with the freqz function:

fs = 1000;                                              % Guess — Not Supplied
Fn = fs/2;                                              
Wp = [0.05 10]/Fn;                                    
Rp =   1;  
[b,a] = cheby1(8,Rp,Wp); 
figure
freqz(b,a, 2^16, fs)

It is always best to use aero-pole-gain representation initially and then second-order-section realisation. Prorotype code that does this for an elliptic filter is:

Fs = 256000;                                                        % Sampling Frequency
Fn = Fs/2;                                                          % Nyquist Frequency
Ws = [48 62]/Fn;                                                    % Stopband Frequency (Normalised)
Wp = [0.99 1.01].*Ws;                                               % Passband Frequency (Normalised)
Rp =  1;                                                            % Passband Ripple
Rs = 90;                                                            % Passband Ripple (Attenuation)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                                     % Elliptic Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp,'stop');                                 % Elliptic Filter Design: Zero-Pole-Gain 
[sos,g] = zp2sos(z,p,k);                                            % Second-Order Section For Stability
figure
freqz(sos, 2^20, Fs)                                                % Filter Bode Plot
set(subplot(2,1,1), 'XLim',Wp*Fn.*[0.8 1.2])                        % Optional

set(subplot(2,1,2), 'XLim',Wp*Fn.*[0.8 1.2])                        % Optional

This creates a stable filter.

Note that frequency-selective filters will only work for band-limited noise. if the signal has broadband noise, wavelet denoising or other appropriate approaches will be required.

MATLAB: How to make this signal linear

If you want to eliminate the low-frequency parabolic(?) trend, the easiest way is to use a digital filter:

signal_2 = load('signal_2.txt');
t = signal_2(:,1);
signal = signal_2(:,2);
figure
plot(signal_2(:,1), signal_2(:,2))
grid
xlabel('Time')
ylabel('signal')
L = numel(t);
Ts = mean(diff(t));
Fs = 1/Ts;
Fn = Fs/2;
FTsignal = fft(signal)/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn;
Iv = 1:numel(Fv);
figure
plot(Fv, abs(FTsignal(Iv))*2)
grid
title('Fourier Transform: ‘signal’')
xlabel('Frequency')
ylabel('Amplitude')
Wp = [25 75]/Fn;                                        % Normailsed Passband (Passband = 25 Hz To 75 Hz)
Ws = [20 80]/Fn;                                        % Normailsed Stopband (Passband = 20 Hz To 80 Hz)
Rp =  1;                                                % Passband Ripple/Attenuation
Rs = 50;                                                % Stopband Ripple/Attenuation
[n,Wp] = ellipord(Wp, Ws, Rp, Rs);                      % Calculate Elliptic Filter Optimum Order
[z,p,k] = ellip(n, Rp, Rs, Wp,'bandpass');              % Elliptic Filter
[sos,g] = zp2sos(z,p,k);                                % Second-Order-Section For Stability
Filtered_signal = filtfilt(sos,g,signal);               % Filter
figure
plot(t, Filtered_signal)
grid
xlabel('Time')
ylabel('Filtered\_signal')

producing:

This filter also eliminates some of the high-frequency noise as well.

Best Answer

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MATLAB: Designing IIR band-pass filter for signal with white noise

MATLAB: How to make this signal linear

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