
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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Estimation