Fourier analysis of waveforms and clipping wave, HELP PLEASE!!!

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Hello all, (Below I have included sample data) So I am working on the fourier spectrum of a waveform. However I need to only take the initial peak of the waveform (the 1 to 1.5 period) of the waveform that I have and achieve a fourier spectrum for that. This has proved to be quite difficult as truncating the waveform is no good as it adds high frequencies to the spectrum. I am clipping the waveform with a find() index command and simply adding a few index values before and after the clip and worked to taper the waveform off using a hamming window (also tried blackman window). There must be a better way of doing this, perhaps building a filter, however I am unsure how to do this. Or perhaps I am doing something else wrong in my calculations. (Sorry for the big question, Been teaching myself matlab for a few months now have been stumped for a while on this problem.)
My code is as follows:
alumdt=1E-8; % Time Step
alumt0=0+alumdt; % Start pick point
alumFs=1/alumdt; % Sampling Frequency
L=9999; % Length
alumt=(0:L-1)*alumdt; % Time array by steps of dt
alumAmplP=alumdata (9:10008,5); % Amplitude Array P wave
NFFT=2^nextpow2(L); % Nyquist Frequecy maybe, length of Fourier window
alumfP=alumFs/2*linspace (0,1,NFFT/2+1);
alumAmplP_2=alumAmplP (1:L); % Amplitude through all steps
alumYP=fft (alumAmplP_2,NFFT)/L;
absalumYP=abs(alumYP);
AlumSpectrum = [transpose(alumfP),2*absalumYP(1:NFFT/2+1)];
absoluteRange = (0:1500:1.25*10^8);
alumYYP = interp1(transpose(AlumSpectrum(1:8193,1)),AlumSpectrum(1:8193,2),absoluteRange);
alumPick = find(alumAmplP > .025, 1, 'first') - 200;
alumPickEnd = alumPick + 600;
alumTimePick = (alumPick*alumdt:alumdt:alumPickEnd*alumdt);
ClippedAlumWave = alumAmplP(alumPick:alumPickEnd);
ClippedAlumT = (alumTimePick);
TaperClippedAlumWave = window(@hamming,numel(ClippedAlumT)).*transpose(ClippedAlumWave)';
%L2 = 319;
alumL2 = length(alumTimePick);
NFFT=2^nextpow2(L); % Nyquist Frequecy maybe, length of Fourier window
alumfP=alumFs/2*linspace (0,1,NFFT/2+1);
ClippedalumAmplP_2=TaperClippedAlumWave; % Amplitude through all steps
ClippedalumYP=fft (ClippedalumAmplP_2,NFFT)/alumL2;
absClippedalumYP = abs(ClippedalumYP);
ClippedAlumSpectrum = [transpose(alumfP),2*absClippedalumYP(1:NFFT/2+1)];
absoluteRange = (0:1500:1.25*10^8);
ClippedalumYYP = interp1(transpose(ClippedAlumSpectrum(1:8193,1)),ClippedAlumSpectrum(1:8193,2),absoluteRange);
figure(1)
subplot(2,1,1)
hold on
plot(alumt, alumAmplP(1:9999))
title('Aluminum Wave-Form')
xlabel('Time (s)')
ylabel('Amplitude')
hold on
line([alumPick*alumdt alumPick*alumdt], [-.15 .15])
line([alumPickEnd*alumdt alumPickEnd*alumdt], [-.15 .15])
subplot(2,1,2)
hold on
plot(absoluteRange,alumYYP)
title('Aluminum Spectrum')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
xlim([0 1.5E6])
figure(2)
subplot(2,1,1)
hold on
plot(ClippedAlumT,TaperClippedAlumWave)
title('Aluminum Wave-Form Initial Peak')
xlabel('Time (s)')
ylabel('Amplitude')
subplot(2,1,2)
hold on
plot(absoluteRange, ClippedalumYYP)
title('(Clip) Aluminum Spectrum')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
xlim([0 1.5E6])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Please help if you can, Thank you so much, Dan
Below I have posted some sample data. the time step for the sample data is 1E-8 = dt
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  1 Comment
Matt Fig
Matt Fig on 26 Oct 2012
Well, I have to give it to you! Usually I have to ask people to provide some data to work with but you did it all on your own. Of course it is so much data that it is a little cumbersome to even view this page....
There is also the option to upload an M-file with all that data in it.

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Accepted Answer

Wayne King
Wayne King on 26 Oct 2012
I'm not sure how you are using the term "period" here. If you are talking about only the first 1 of the fundamental frequency which is 1 MHz here, then I think you want at least a few periods to do a spectral analysis even with a clean waveform. The resolution in the DFT (implemented by fft) depends on the number of samples. The more samples, the better the resolution.
In your case, it's easy to see that
xnew = x(1:2800);
gives you the initial waveform, so why not use this?
Fs = 1/1e-8;
d = fdesign.lowpass('Fp,Fst,Ap,Ast',1.2e6,1.4e6,0.5,60,Fs);
Hd = design(d,'butter');
xnew = x(1:2800);
y = filter(Hd,detrend(xnew,0));
ydft = fft(y);
freq = 0:Fs/length(y):Fs/2;
ydft = ydft(1:floor(length(y)/2)+1);
% Plot in MHz
plot(freq./1e6,abs(ydft))
axis([0 10 0 max(abs(ydft))+20])
xlabel('MHz'); ylabel('Magnitude');
If you copy and paste the above code, it works fine.
  2 Comments
Dan
Dan on 26 Oct 2012
Sorry for the confusion, I had been throwing around the word period fairly loosely. By one period/initial wavelet I meant that I can only use say xnew from ~xnew(1:1850). And if I just cut the waveform there then high frequencies are added, so I need some way to taper it out there.
After that xnew(1:1850) the wave is mish mesh of reflections and wave so cant use it.
Wayne King
Wayne King on 26 Oct 2012
Edited: Wayne King on 26 Oct 2012
It doesn't matter if you only take 500 points of this signal. The signal is not a pure sine wave so there is no way you'll only get energy at 1 MHz. If you look at this signal, there is clearly harmonic structure. So you will always have harmonics of 1 MHz in this data. This should not bother you because the sine wave is a model that you don't get with real data except in very tightly controlled situations. It is true in your case that the spurious free dynamic range (the ratio of power between the fundamental and the next most powerful harmonic) is not very big, but you can filter out the higher harmonics. It's not the truncation that is causing these harmonics to appear. It's that the data are not inherently a perfect sine wave.

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More Answers (1)

Wayne King
Wayne King on 26 Oct 2012
You clearly have a strong oscillation at 1 MHz in the data and strong harmonics of that fundamental. Do you have the Signal Processing Toolbox? If so, yes, you can easily apply a lowpass filter that will remove the higher harmonics.
Fs = 1/1e-8;
d = fdesign.lowpass('Fp,Fst,Ap,Ast',1.2e6,1.4e6,0.5,60,Fs);
Hd = design(d,'butter');
% let x be the data record given above in your post
y = filter(Hd,detrend(x,0));
ydft = fft(y);
freq = 0:Fs/length(y):Fs/2;
ydft = ydft(1:floor(length(y)/2)+1);
% Plot in MHz
plot(freq./1e6,abs(ydft))
axis([0 10 0 max(abs(ydft))+20])
xlabel('MHz'); ylabel('Magnitude');
  4 Comments
Dan
Dan on 26 Oct 2012
This seems to work as a good noise filter, however my task is to truncate (clip) the waveform taking only the first initial arrival and obtain the amplitude frequency spectrum of this initial peak. Because clipping a wave adds high frequencies to the fourier spectrum I need to find a way around simply clipping and then performing an FFT to the clipped wave segment.
The waveform sample data I posted above is an induced waveform with many reflections following it (as this is a wave traveling through a piece of aluminum). So in order to only take obtain the true induced wave spectrum (no reflections) I must use only the first initial wave pulse (the first up and down of the wave, 1 period to 1.5) I am also not sure if there is a way to get matlab to pick out the first period or 1.5 period as I am giving eyeballed indicies to tell it where to clip and then trying to taper with a (very) basic hamming window and then performing the FFT. This seems to be a very inconsistent (and not working well) way of going about this.

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