Lecture 9_winter_2012

Lecture 9_winter_2012 - Digital Speech Processing Lecture 9...

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1 Digital Speech Processing— Lecture 9 Short-Time Fourier Analysis Methods- Introduction
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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)
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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
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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)
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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
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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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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
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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: ( ) ( ) ( ) () ( ) ( ) , jj m m L jL k m m Xe xme DTFT Xk xmwme ωω π =−∞ = = = ± (2 / ) 0,1,. .., 1 ( ) using a value of =25000 we get the following plot j kL DFT L ω ωπ = = = ±
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9 25000-Point DFT of Speech Magnitude Log Magnitude (dB)
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Short-Time Fourier Transform (STFT) 10
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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
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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 ( ) ωω ω =−∞ =− •− jj m n m j n Xe x m w n m e n wn m xn
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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 - Digital Speech Processing Lecture 9...

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