Mel-Frequency Cepstral Coefficients (MFCCs)

Mel-Frequency Cepstral Coefficients (MFCCs)

참고 : https://www.youtube.com/watch?v=fMqL5vckiU0&list=PL-wATfeyAMNrtbkCNsLcpoAyBBRJZVlnf

1. Introduction

Mel-Frequency Cepstral Coefficients

• Cepstral: Cepstrum \(\leftrightarrow\) Spectrum

How to compute Cepstrum?

\(C(x(t))=F^{-1}[\log (F[x(t)])]\).

2. Vocal tract

Vocal Tract acts as a filter of a speech

• vocal tract (성도) : 소리가 나가는 길

3. Decomposing Speech

\(\rightarrow\) Peaks of spectral envelope, or formants, carry the identity of sound!

We can see “speech” as a “convolution of (1) with (2)”

• (1) vocal tract frequency response
• (2) glottal pulse

\(X(t)=E(t) \cdot H(t)\).

\(\log (X(t))=\log (E(t) \cdot H(t))\).

\(\log (X(t))=\log (E(t))+\log (H(t))\).

4. Liftering

Removing the high quefruency values! ( or the “glottal pulse” )

5. Calculating MFCCs

Waveform \(\rightarrow\) DFT \(\rightarrow\) Log-amplitude Spectrum \(\rightarrow\) Mel-scaling \(\rightarrow\) Discrete cosine transform

But why use discrete cosine transform?

( = similar to inverse transform )

• simplfied version of FT
• get real-valued coefficient
• decorrelate energy in different mel bands
• reduce # of dim to represent spectrum

How many coefficients to use?

• First 12~13 coefficients ( low frequencies )

  • 1st : Most information
    • corresponds to “formants”, “spectral envelope”
  • Last : Least information

• Use \(\Delta\) and \(\Delta \Delta\) MFCCs

  \(\rightarrow\) about 39 coffeicients per frame

Visualization