Lecture 9_winter_2012_6tp

Lecture 9_winter_2012_6tp - General Discrete-Time Model of...

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1 1 Digital Speech Processing— Lecture 9 Short-Time Fourier Analysis Methods- Introduction 2 General Discrete-Time Model of Speech Production Voiced Speech: A V P(z)G(z)V(z)R(z) Unvoiced Speech: A N N(z)V(z)R(z) 3 Short-Time Fourier Analysis • represent signal by sum of sinusoids or complex exponentials as it leads to convenient solutions to problems (formant estimation, pitch period estimation, analysis-by-synthesis methods), and insight into the signal itself • such Fourier representations provide – convenient means to determine response to a sum of sinusoids for linear systems – clear evidence of signal properties that are obscured in the original signal 4 Why STFT for Speech Signals • steady state sounds, like vowels, are produced by periodic excitation of a linear system => speech spectrum is the product of the excitation spectrum and the vocal tract frequency response • speech is a time-varying signal => need more sophisticated analysis to reflect time varying properties – changes occur at syllabic rates (~10 times/sec) – over fixed time intervals of 10-30 msec, properties of most speech signals are relatively constant (when is this not the case) 5 Overview of Lecture • define time-varying Fourier transform ( STFT ) analysis method • define synthesis method from time-varying FT (filter-bank summation, overlap addition) • show how time-varying FT can be viewed in terms of a bank of filters model computation methods based on using FFT application to vocoders, spectrum displays, format estimation, pitch period estimation 6 Frequency Domain Processing Coding : – transform, subband, homomorphic, channel vocoders Restoration/Enhancement/Modification : – noise and reverberation removal, helium restoration, time-scale modifications (speed-up and slow-down of speech)
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2 7 Frequency and the DTFT 00 0 0 2 sinusoids ( ) cos( ) ( )/ where is the (in radians) of the sinusoid the Discrete-Time Fourier Transform ( ) ( ) ( ) ( frequency ωω ω =−∞ == + jn jj n n xn n e e Xe xne x {} 1 2 -1 ) () ( ) where is the of ( ) frequency variable π n j j n Xe e d 8 DTFT and DFT of Speech 1 (2 / ) 0 The DTFT and the DFT for the infinite duration signal could be calculated (the DTFT) and approximated (the DFT) by the following: ( ) ( ) ( ) ( )( ) , m m L jL k m m xme Xk xmwme =−∞ = = = ± (2 / ) 0,1,. .., 1 using a value of =25000 we get the following plot j kL DFT L ωπ = =− = ± 9 25000-Point DFT of Speech Magnitude Log Magnitude (dB) Short-Time Fourier Transform (STFT) 10 11 Short-Time Fourier Transform • speech is not a stationary signal , i.e., it has properties that change with time • thus a single representation based on all the samples of a speech utterance, for the most part, has no meaning • instead, we define a time-dependent Fourier transform (TDFT or STFT) of speech that changes periodically as the speech properties change over time 12 Definition of STFT ˆˆ ˆ ˆ ˆ ˆ ( ) ( ) ( ) both and are variables ( ) is a real window which determines the portion of ( ) that is used in the computation of ( ) =−∞ •− m n m j n
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This note was uploaded on 12/29/2011 for the course ECE 259 taught by Professor Rabiner,l during the Fall '08 term at UCSB.

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Lecture 9_winter_2012_6tp - General Discrete-Time Model of...

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