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Unformatted text preview: Digital Speech Processing Digital Speech Processing— Lecture 11 Lecture 11 Modifications, Filter Bank Modifications, Filter Bank Design Methods Design Methods 1 odifications to STFT odifications to STFT Modifications to STFT Modifications to STFT modifications to shorttime spectrum can be fixed (nontime varying) or timevarying • fixed modification (no variability with ) ˆ ( ) ( ) ( ) ω ω ω • = ⋅ k k k j j j n n n X e X e P e assume inverse DFT of ( ) exists ω • k j P e 1 1 , then [ ] ( ) ω ω − k k N j j n n P e e [ ] ( ) where is the number of frequencies at which = = • ∑ k p n P e e N N 2 ( ) is evaluated ω k j P e ixed Modifications using FBS ixed Modifications using FBS Fixed Modifications using FBS Fixed Modifications using FBS using FBS methods we get • 1 ˆ [ ] ( ) ( ) ω ω ω − = = ∑ k k k N j j j n n k y n X e P e e 1 [ ] [ ) ( ) ω ω ω − ∞ − = = − ∞ ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ∑ ∑ k k k N j m j j n k m w n m x m e P e e 1 ( ) [ ] ( ) ( ) ω ω ∞ − − =−∞ = ⎡ ⎤ = − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ∑ ∑ k k N j j n m m k w n m x m P e e [ ] [ ] [ ] ∞ =−∞ = − − ∑ m w n m x m N p n m 3 ˆ [ ] [ ] [ = ∗ y n Nx n w n ] [ ] ⋅ ⎡ ⎤ ⎣ ⎦ p n ixed Modifications using FBS ixed Modifications using FBS Fixed Modifications using FBS Fixed Modifications using FBS ˆ [ ] [ ] [ ] [ ] = ∗ ⋅ ⎡ ⎤ ⎣ ⎦ y n Nx n w n p n ˆ [ ] [ ] convolved with [ ] [ ] equivalent to linear filtering operation on [ ] • = ⋅ = > ⎡ ⎤ ⎣ ⎦ y n x n w n p n x nid eall y want [ ] [ ] [ ] need duration of [ ] duration of [ ] [ ] is = ∗ ⇒ ¡ ¢ y n x n p n p n w n n periodic sequence of period (sampled [ ] is • p n a periodic sequence of period (sampled in frequency at frequencies) if [ ] is longer than repetitive structure in • = > N N w n N [ ] [ ] [ ] need to avoid long filters (IIR) but instead use ⋅ = = > p p n w n h n RW so that 4 1 [ ] [ ] [ ] [ ], = ⋅ ≈ ≤ ≤ − p h n p n w n p n n N ime ime arying Modifications arying Modifications Time Time Varying Modifications Varying Modifications epresent timevarying modification as represent timevarying modification as ˆ ( ) ( ) ( ) with timevarying IR, ( ), defined as ω ω ω • = ⋅ • k k k j j j n n n n X e X e P e p m 1 1 [ ] ( ) ω ω − = = ∑ k k N j j m n n k p m P e e N 1 ˆ solve for [ ] as ˆ [ ] ( ) ( ) ω ω ω − • = ∑ k k N j j j n n y n y n X e P e e k n = k 1 [ ] [ ] ( ) ω ω ω ω − ∞ − = − ∞ = − ∑ ∑ k k k k N j n j m j j n n m e x n m w m e P e e 5 = = − ∞ k m ime ime arying Modifications arying Modifications Time Time Varying Modifications Varying Modifications 1 − ∞ N 1 ˆ [ ] [ ] [ ] ( ) [ ) [ ] ( ) ω ω ω ω ω ω − = = − ∞ ∞ − = − = − ∑ ∑ ∑ ∑ k k k k k k j n j m j j n n k m N j j m n y n e x n m w m e P e e x n m w m P e e [ ] [ ] [ ] =−∞ = ∞ =−∞ = − ∑ ∑ ∑ m k n m x n m w m Np m ˆ [ ] [ ] [ ] [ ] [ ]...
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 Fall '08
 Rabiner,L
 Digital Signal Processing, Signal Processing, Lowpass filter, Finite impulse response, Filter Bank, STFT

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