matlab signals signal-processing fft spectrum

Spectrum Analysis of 1D Signal (FFT etc.)

I have two Signals: a noisy Input-Signal and a filtered OutputSignal. The Noise-Filter has been implemented with a Kalman-Filter.

Please click on the link below to see the signals!

As I see it, the Signals have two main Frequencies: first of all the big waves with a period of about 75 units and the small noise with a period of 4-5 units. The implemented filter only reduces the noise with small wavelengths.

For a presentation I want to visualize the spectrum of the two signals to show the influence of the filter on different wavelengths.

I tried to use the Matlab Fourier-Function 'fft' but the result did not represent the two frequencies at all. I also tried the MatlabTool 'sptool' without convincing results. The online Tool 'Fourier Calculator from sooeet' gave different results but not what I expected either. I tried all these tool but the spectrums always looked completely random and noisy.

What I would like to see is a spectrum composed of low frequencies and high frequencies (as you see in the linked picture), but all of the algorithms/tools tested looked totally different:

I outlined my expectations on the linked picture below.

the two signals and my expectation of the spectrum

Perhaps somebody knows a tool that can calculate the frequencies like this.

The values of the Signals are:

and:

Thanks in advance!

Solution

You can display the data in a way that makes the effect of the filter more clear.

Try the following alternatives:

Nt = length(signal1); % same as for signal2
Nf=2^nextpow2(Nt);
f = [0:Nf/2]/Nf;
spec1 = fft(signal1,Nf);
spec2 = fft(signal2,Nf);

(1) log/abs combination:

figure
semilogy(f,abs(spec1(1:Nf/2+1)))
hold on
semilogy(f,abs(spec2(1:Nf/2+1)),'g')
axis tight

(2) ratio:

figure
plot(f,abs(spec2(1:Nf/2+1))./abs(spec1(1:Nf/2+1)))
axis tight

Results are shown in the plots below:

enter image description here

Note that the signals with periodicity 75 and 5 time units should show up at ~0.013 and 0.2 frequency units, respectively.