{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch7-Short-Time_Fourier_Transform_Analysis_and_Synthesis

Ch7-Short-Time_Fourier_Transform_Analysis_and_Synthesis -...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Speech Processing Short-Time Fourier Transform  Analysis and Synthesis
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2/13/12 Veton K ë puska 2 Short-Time Fourier Transform  Analysis and Synthesis:  Minimum-Phase Synthesis u Speech & Audio Signals are varying and can be considered stochastic  signals that carry information. u This necessitates short-time analysis since a single Fourier transform  (FT) can not characterize changes in spectral content over time (i.e.,  time-varying formants and harmonics) n Discrete-time short-time Fourier transform (STFT) consists of separate FT of  the signal in the neighborhood of that instant. n FT in the STFT analysis is replaced by the discrete FT (DFT) Resulting STFT is discrete in both time and frequency. Discrete  STFT vs. Discrete-time  STFT which is continuous in frequency. u In linear Prediction and Homomorphic Processing, underlying model of  the source/filter is assumed. This leads to:  n Model based analysis/synthesis, also note that n Analysis methods presented implicitly both used short time analysis methods  (to be presented). u In Short-Time Analysis systems no such restrictions apply.
Background image of page 2
2/13/12 Veton K ë puska 3 Short-Time Analysis (STFT) u Two approaches of STFT are explored: 1. Fourier-transform & 2. Filterbank
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Fourier Transform View 2/13/12 Veton K ë puska 4
Background image of page 4
2/13/12 Veton K ë puska 5 Fourier-Transform View u Recall (from Chapter 3): u w[n] is a finite-length, symmetrical  sequence (i.e., window) of length Nw.  n w[n]   0 for [0, Nw-1] n w[n] – Analysis window or Analysis Filter ( 29 [ ] [ ] -∞ = - - = m n j e m n w m x n X ϖ ϖ ,
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2/13/12 Veton K ë puska 6 Fourier-Transform View u x[n] – time-domain signal u fn[m]=x[m]w[n-m]  - Denotes short-time section of  x[m] at point n. That is, signal at the frame n. u X(n,w ) - Fourier transform of fn[m] of short-time  windowed signal data. u Computing the DFT: ( 29 ( 29 k N n X k n X π ϖ ϖ 2 | , , = =
Background image of page 6
2/13/12 Veton K ë puska 7 Fourier-Transform View u Thus X(n,k) is STFT for every w =(2p /N)k n Frequency sampling interval  = (2p /N) n Frequency sampling factor  = N u DFT: ( 29 [ ] [ ] -∞ = - - = m km N j e m n w m x k n X π 2 ,
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Fourier-Transform View 2/13/12 Veton K ë puska 8 a) Speech waveform x[n] (blue) Window function w[n] (red) b) Windowed section of speech c) It’s Magnitude Spectrum. 
Background image of page 8
2/13/12 Veton K ë puska 9 Example 7.1 u Let x[n] be a periodic impulse train sequence: u Also let w[n] be a triangle of length P: -∞ = - = l lP n n x ] [ ] [ δ P 2P 3P -P 0 n P/2+1 -P/2 P-points n
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2/13/12 Veton K ë puska 10 Example 7.1 lP j l m m j l m m j e lP n w e m n w lP m e m n w m x n X ) ( ] [ ) ( ] [ ] [ ) , ( ϖ ϖ ϖ δ ϖ - -∞ = -∞ = - -∞ = -∞ = - - = - - = - = Non-zero only for  m= lP Window located at  lP   & Linear phase -w lP
Background image of page 10
2/13/12 Veton K ë puska 11 Example 7.1 u
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}