DATAWRAP

I've noticed that MATLAB uses datawrap to compute spectra (or spectrum-related quantities) when the user asks for a number NFFT of frequencies that is smaller than the WINDOW-LENGTH/2+1 (if WINDOW-LENGTH is even) rule. Essentially datawrap chuncks the data into smaller segments and then averages the segments together. Am I right? Since I think that this would really be bad for my data: why is it implemented like that? and why is it not documented in the helps? Many thanks in advance, Cesare

[Honglei Chen]

Could you be more specific about where you see this? I don't see why WINDOW-LENGTH/2 is so special. Maybe I'm missing something.

Answer 1

[Cesare]

I'll try to be more precise. For real time series of length N the spectral functions usually return N/2+1 frequency bins if N is even and (N+1)/2 if N is odd. However, functions as SPECTROGRAM have the option to specify the number of output bins through an input variable which is usually called NFFT. I digged into the code and found out that what these functions do when NFFT is smaller then the default number of bins, is to wrap the data. This means that the data array is cut into smaller chuncks which are then averaged together. This is not documented in the function help and I wonder whether it is good practice. Cesare

Answer 2

[Honglei Chen]

Hi Cesare,

If I understand your question correctly, your problem is more related to why MATLAB wrap the data, the particular length is just a specific case. I'll try to explain the reason for wrapping the data.

The calculation of signal spectrum, such as periodogram, uses FFT internally, where the length of FFT is denoted as NFFT. In theory, when using FFT, the signal in both time domain and frequency domain are discrete and periodic, where the period is given by NFFT. Hence, if you specify an NFFT that is less than the signal length, it actually introduces the aliasing in the time domain and make the signal (even if its length is N>NFFT) periodic with NFFT. When you take FFT of this sequence, you are working with this aliased sequence. This is what datawrap do for you.

For example, if you have a sequence 1 2 3 4 5, assuming that your period is also 5, you have

1 2 3 4 5
          1 2 3 4 5
                    1 2 3 4 5
--------------------------------
      ... 1 2 3 4 5 ...

i.e., your original series. Now assume you have a period of 3, then it looks like

1 2 3 4 5
      1 2 3 4 5
            1 2 3 4 5
------------------------
  ... 5 7 3 ...

A sequence that is wrapped around and has only a length of 3. Note that

>> datawrap(1:5,3)
ans =
     5     7     3

HTH.

Answer 3

[Cesare]

The signal need not be periodic, take for example autoregressive models. They have a very well defined periodogram but are not necessarily periodic. I believe that the internal wrapping could end up in dangerous phase cancellation without the user knowing it. Cesare

[Honglei Chen]

Your signal may not be periodic to start with. But if you use FFT, it samples the signal in both time and frequency, which in turn makes the signal periodic in both frequency and time, and that's where the circular convolution behavior kicks in.

Answer 4

[Zeeshan Salam]

how i wrap these two curves?

%define x for both curves

x_ref = 0:0.01:1;

x = 0:0.01:1;

%define the reference curve and the other curve

c_ref = sin(x_ref*2*pi);

y = 0.5+0.5*sin(x*2*pi);

%plot both curves

figure(1)

plot (x_ref,c_ref,'r');

hold on

plot(x,y,'b');

axis([min(x_ref)-1,max(x_ref)+1,min(c_ref)-1,max((c_ref))+1]);

legend('c_{ref}','y')