Cepstral Windowing
The spectral envelope obtained by cepstral windowing is defined as
![$\displaystyle Y_m \eqsp \hbox{\sc DFT}[w \cdot \underbrace{\hbox{\sc DFT}^{-1}\log(\vert X_m\vert)}_{\hbox{real cepstrum}}]$](http://www.dsprelated.com/josimages_new/sasp2/img1728.png) |
(11.2) |
where
is a lowpass-window in the cepstral domain. A simple but
commonly used lowpass-window is given by
![$\displaystyle w(n) \eqsp \left\{\begin{array}{ll} 1, & \vert n\vert< n_c \\ [5pt] 0.5, & \vert n\vert=n_c \\ [5pt] 0, & \vert n\vert>n_c, \\ \end{array} \right.$](http://www.dsprelated.com/josimages_new/sasp2/img1729.png) |
(11.3) |
where
denotes the lowpass ``cut-off'' sample.
The log-magnitude spectrum of 
is thus lowpass filtered
(the real cepstrum of 
is ``liftered'') to obtain a smooth spectral
envelope. For periodic signals,
should be set below the period
in samples.
Cepstral coefficients are typically used in speech recognition
to characterize spectral envelopes, capturing primarily
the formants (spectral resonances) of speech [227].
In audio applications, a warped frequency axis, such as the ERB
scale (Appendix E), Bark scale, or Mel frequency scale is
typically preferred. Mel Frequency Cepstral Coefficients (MFCC)
appear to remain quite standard in speech-recognition front ends, and
they are often used to characterize steady-state spectral timbre in
Music Information Retrieval (MIR) applications.
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