0
$\begingroup$

I am currently working with non-audio signals of which I would like to calculate the Cepstrum coefficients with Python so that I can use them with machine learning algorithms. That's probably a quite basic question, but somehow I'm struggling at this point.

I already found some packages in Python that can be used to calculate the MFCCs. However, since these refer to the Mel Frequency, they are unfortunately not suitable for my application.

I already found out that the cepstrum of the signal can be calculated in Python as follows (from this website):

powerspectrum = np.abs(np.fft.fft(signal))**2
cepstrum = np.fft.ifft(np.log(powerspectrum))

That's working so far. But with which formula do I get the (n first) cepstral coefficients?

(I know that I should apply a window function on the signal first - my question is mainly about the approach to calculate the cepstral coefficients)

$\endgroup$
  • $\begingroup$ Apply DCT, right? $\endgroup$ – jojek May 2 '18 at 9:03
  • $\begingroup$ Thanks for your help! I found out by now, that there seems to be not a single definition of cepstral coefficients. But applying the DCT to the cepstrum seems to be a common way to get cepstral coefficients. $\endgroup$ – Frank May 7 '18 at 8:28
1
$\begingroup$

Linear Prediction Cepstral Coefficients (LPCC) can easily be computed from LPC (Linear Prediction Coefficients) and I think that a LPC function is implemented in the same package as the MFCC.

All you need to know for extracting $p + 1$ first LPC is here. The formula that link LPC and LPCC is:

$c_0 = ln(p)$

$c_1 = a_1$

$c_i = -a_i + \sum_{n=1}^{i-1}\frac{n}{i}a_{i-n}c_n$ for $1 < i \leq p$

where $c_i$ are the LPCC and $a_i$ the LPC and $p$ the order (i.e. the number of coefficients - 1). I'm not sure about the negative sign before $a_1$. Reference here.

I'm not sure what you mean with 'windowing' but yes it may be necessary depending on your signal and application.

Hope that it will help.

$\endgroup$
  • $\begingroup$ Thanks for your help! If somebody else is also looking for this: to get the LPC and LPCC, this python package was helpful for me: github.com/RicherMans/pymir $\endgroup$ – Frank May 7 '18 at 8:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.