MATLAB: Finding different length pulses

MATLABpulses

I have attached a screen shot of some pulses with diiferent lenghts my question is what is the best way clean these up and show them.

Thank You

David

Best Answer

Note that ‘clean them up’ is ever so slightly ambiguous.

Assuming that the objective is to remove some of what might be considered ‘noise’, first calculate the Fourier transform of the signal, then using that information to determine where the ‘noise’ frequencies begin, design a lowpass filter to remove the undesirable higher frequencies. (For all of these, the sam;ing intervals must be constant. If it is not, use the resample function to interpolate them to a constant sampling frequency first.)

The Fourier transform is straightforward (assuming ‘x’ is the signal vector):

Fs = ... ;                                      % Sampling Frequency (Hz)
Fn = Fs/2;                                      % Nyquist Frequency (Hz)
L = numel(x);                                   % ‘x’ Is A Vector
xm = mean(x);
xfft = fft(x - xm)/L;                           % Subtract Mean & Normalise By ‘L’
Fv = linspace(0, 1, fix(L/2)+1)*Fn;             % Frequency Vector
Iv = 1:numel(Fv);                               % Index Vector
figure
plot(Fv, abs(xfft(Iv))*2)
grid
xlabel('Frequency (Hz)')
ylabel('Magnitude')

With that information, use the lowpass function to design the filter, or use command-line arguments in a script to design your own filter. This is straightforward with the Signal Propcessing Toolbox functions.

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MATLAB: About Butterworth filter design

You have not clearly stated what you want to do.

You also have problems in your calculations, and your data are not uniformly sampled.

First, you need to use the Signal Processing Toolbox resample (link) function to regularly sample your data. Create a time vector for the resampling (interpolation) as:

tv = linspace(min(date), max(date), size(data,1));

From the documentation:

y = resample(x,tx) resamples the values, x, of a signal sampled at the instants specified in vector tx. The function interpolates x linearly onto a vector of uniformly spaced instants with the same endpoints and number of samples as tx. NaNs are treated as missing data and are ignored.

Second, you are not calculating the sampling interval and therefore the sampling frequency correctly. Calculate them as:

Ts = mean(diff(tv));                                    % Sampling Interval (Days)
Fs = 1/Ts;                                              % Sampling Frequency (1/Day)
Fn = Fs/2;                                              % Nyquist Frequency (1/Day)

Then do a fft (link) on your resampled data to determine the frequencies you want to pass or reject, and specify your filter accordingly. I cannot do that because I do not know what you want to do.

Use the filtfilt function, not filter, to do the actual filtering.

MATLAB: How to calculate passband and stopband coefficients for signal filtering

Specifying both passband and stopband frequencies (and without other arguments to the ellip function) means that you are designing a bandpass filter. I appreciate your quoting my code, however I also posted several examples of elliptical filters using bandpass filters.

For your filter, replace ‘Wp’ with:

Wp = [250  512]/Fn;                                             % Passband Frequencies For Bandpass Filter (Hz)

and ‘Ws’ with:

Ws = [0.99 1.01]*Wp;                                            % Stopband Frequencies For Bandpass Filter (Hz)

or define it yourself, similarly to the way I defined ‘Wp’ here. Note that for a bandpass filter, the stopbands must be outside the passbands.

Best Answer

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