inconsistency in the algorithm for calculating cross spectral densities

[zsoltlazar]

Bug report

Bug summary

In /usr/local/lib/python2.7/dist-packages/matplotlib/mlab.py Welch's periodogramm method is implemented erronously for the case of two time series. For the second time series the order of detrending and windowing are interchanged.

between lines 716 to 728, within the _spectral_helper method

    result = detrend(result, detrend_func, axis=0)    // ZIL comment: detrend first 
    result, windowVals = apply_window(result, window, axis=0,  // ZIL comment: windowing next
                                      return_window=True)      // THIS IS CORRECT!
    result = np.fft.fft(result, n=pad_to, axis=0)[:numFreqs, :]
    freqs = np.fft.fftfreq(pad_to, 1/Fs)[:numFreqs]

    if not same_data:
        # if same_data is False, mode must be 'psd'   
        resultY = stride_windows(y, NFFT, noverlap)
        resultY = apply_window(resultY, window, axis=0)  // ZIL comment: windowing first ????? 
        resultY = detrend(resultY, detrend_func, axis=0) // ZIL comment: detrend next ??????
                                                                  // THIS IS INCORRECT!
        resultY = np.fft.fft(resultY, n=pad_to, axis=0)[:numFreqs, :]
        result = np.conjugate(result) * resultY

Matplotlib version

• Operating system: Ubuntu 16.04
• Matplotlib version: 2.0.1
• Python version: 2.7.12

[jklymak]

What to do about these fcns is an interesting conversation, because users really should be using the numpy functions. I think these ones are a historic artifact.

That said, I agree this is wrong, and I just checked, that it is indeed wrong in master. Did you want to try a PR to fix it. If not, I'm happy to do it.

[zsoltlazar]

Thank you for the feedback!
I don't have experience in working with these repositories. So you can go ahead and correct it if you have the resources.

[dstansby]

Fixed by #9753