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Cepstral Smoothing


\epsfig{file=eps/cep-smooth.eps}

The spectral envelope obtained by cepstral smoothing is defined as

$\displaystyle Y_m = \hbox{\sc DFT}[w \cdot \underbrace{\hbox{\sc DFT}^{-1}\log(\vert X_m\vert)}_{\hbox{real cepstrum}}]
$

where $ w$ is a lowpass window in the cepstral domain, e.g.,

$\displaystyle w(n) = \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.
$


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``Cross Synthesis Using Cepstral Smoothing or Linear Prediction for Spectral Envelopes'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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