Question

For this type of data I want to do an interpolation like fit from one maxima to a minima and so on, so I can look for superimposed high frequencies:

I have a matrix of values such as:

a=[ 3 7 10 3 1 5 10 5  3 2 4 8 10 7 4 3 4 2 1 4 5 7 10 8 7 6 6 4 3 2];

Now I want to choose the relative and maximum and minimum values such that

a=[ 3 0 10 0 1 0 10 0  0 2 0 0 10 0 0 0 0 0 1 0 0 0 10 0 0 0 0 0 0 2];

I essentially want to fit a straight line from a(1) to a(3) and then from a(3) to a(5) and so on, and then subtract the fit from the data.

I know there is a function “detrend” that uses a breakpoint method it denotes as “bp”, and that is the closest thing I found resembling my goal.

If you know of a way MATLAB can do this I will greatly appreciate it, otherwise it seems like I have to write an m-file to do it.

Answer 1

I think what your question is asking for is interpolation between the local minima and local maxima of a time series (what you call the “relative minimum and maximum values”.)

See this similar question and add some code that does a linear interpolation between the local minima and maxima.

interp1() will do this handily. There is no need for the input points or the output points to be evenly spaced.

>> x = sort(rand(1,10));
>> y = rand(1,10);
>> plot (x,y,'r.');
>> xx = 0:0.01:1;
>> yy = interp1(x,y,xx);
>> hold on;
>> plot (xx,yy,'b-')

---

What I think you really want to do is decompose the signal into components based on local time scale. (that is, where the frequencies change with time). Use the empirical mode decomposition. Wavelet methods might be an alternative, but the output of the EMD is very easy to interpret visually.

---

Incidentally, the plain FFT won’t work if applied to the entire length of a signal that is time varying – the FFT assumes a stationary (non-varying) signal.

You need to apply the Short-Time Fourier Transform, which is the FFT applied over sliding windows of the data to get a picture of frequency over time. See the spectrogram() function.

>> plot (x,y)
>> x=0:0.001:1;
>> y = chirp(x);
>> plot (x,y);
>> figure;
>> spectrogram(y);

There are issues with time vs. frequency resolution of the short-time Fourier transform that limit its application when your sampling rate is low compared to the frequency of the data. It would would be unlikely to work well for the example data you posted a picture of.