Lecture14 - Lecture 14 EE214A Abeer Alwan Recall the LTI...

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1 Lecture 14 EE214A Abeer Alwan Recall the LTI Model of Speech Production
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2 Analysis Techniques Studies Thus Far We have studied how to analyze the speech signal using time-domain features and by using the STFT and LPC The STFT provides temporal-spectral analysis of the signal while LPC provides an estimate of the underlying LTI Vocal Tract Transfer Function assuming it is all pole. Homomorphic (Cepstral) Analysis -Chapter 8- Originally thought of as a deconvolution method First introduced for echo cancellation Today used in a variety of applications including speech and speaker recognition
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3 Terminology Spectrum Fourier transform of signal Cepstrum Inverse Fourier transform of log spectrum Filtering operations on spectrum Liftering operations on cepstrum Frequency basic unit of spectrum Quefrency basic unit of cepstrum Analysis operation on spectrum Alanysis operation on cepstrum Homomorphic (Cepstral) Analysis )] ( [ )] ( [ )] ( ) ( [ 2 1 2 1 n x bL n x aL n bx n ax L 1 2 1 2 1 2 1 2 ( ) ( )* ( ) then ˆ ˆ ˆ ( ) ( ) ( ) ˆ ˆ ˆ where ( ), ( ), ( ) are the cepstra of ( ), ( ), and ( ), respectively y n x n x n y n x n x n y n x n x n y n x n x n For a linear system (L), we have: If now the two signals are convolved:
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4 Homomorphic Analysis ) ( * ) ( ) ( If n p n t n x )] ( [ * )] ( [ )] ( * ) ( [ Then n p H n t H n p n t H )]]] ( * ) ( [ [ [ )] ( * ) ( [ 1 n p n t D L D n p n t H For a Homomorphic system : Representation of a system obeying the superposition principle for addition. Such systems will be termed “conventional linear systems.”
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5 Representation of a homomorphic system for convolution.
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