This preview shows pages 1–11. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Speech Processing ShortTime Fourier Transform Analysis and Synthesis 2/13/12 Veton Këpuska 2 ShortTime Fourier Transform Analysis and Synthesis: MinimumPhase Synthesis u Speech & Audio Signals are varying and can be considered stochastic signals that carry information. u This necessitates shorttime analysis since a single Fourier transform (FT) can not characterize changes in spectral content over time (i.e., timevarying formants and harmonics) n Discretetime shorttime 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. ⇒ Discretetime 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 ShortTime Analysis systems no such restrictions apply. 2/13/12 Veton Këpuska 3 ShortTime Analysis (STFT) u Two approaches of STFT are explored: 1. Fouriertransform & 2. Filterbank Fourier Transform View 2/13/12 Veton Këpuska 4 2/13/12 Veton Këpuska 5 FourierTransform View u Recall (from Chapter 3): u w[n] is a finitelength, symmetrical sequence (i.e., window) of length Nw. n w[n] ≠ 0 for [0, Nw1] n w[n] – Analysis window or Analysis Filter ( 29 [ ] [ ] ∑ ∞∞ = = m n j e m n w m x n X ϖ ϖ , 2/13/12 Veton Këpuska 6 FourierTransform View u x[n] – timedomain signal u fn[m]=x[m]w[nm]  Denotes shorttime section of x[m] at point n. That is, signal at the frame n. u X(n,w )  Fourier transform of fn[m] of shorttime windowed signal data. u Computing the DFT: ( 29 ( 29 k N n X k n X π ϖ ϖ 2  , , = = 2/13/12 Veton Këpuska 7 FourierTransform 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 , FourierTransform View 2/13/12 Veton Këpuska 8 a) Speech waveform x[n] (blue) Window function w[n] (red) b) Windowed section of speech c) It’s Magnitude Spectrum. 2/13/12 Veton Këpuska 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 3PP n … P/2+1P/2 Ppoints n 2/13/12 Veton Këpuska 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 ∞∞ = ∞∞ = ∞∞ = ∞∞ = ∑ ∑ ∑ ∑ =  = =...
View
Full
Document
This note was uploaded on 02/11/2012 for the course ECE 5525 taught by Professor Staff during the Fall '10 term at FIT.
 Fall '10
 Staff

Click to edit the document details