Lecture8 - Lecture 8 EE214A Abeer Alwan Signal...

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1 Lecture 8 EE214A Abeer Alwan Signal Reconstruction Filterbank Summation (FBS) Overlap and Add (OLA)
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2 ) ( | ) ( | ) ( ) ( ) ( ) ( ) ( n j j n n n m m j j n e e X jb a e m n w m x e X Recall that the Short Time Fourier Transform (STFT) is defined as: fixed: m m j j n e m n w m x e X ) ( ) ( ) ( The STFT can then be thought of as the convolution of the functions : ) ( ) ( n w e n x n j ) ( n w n j e ) ( n x ) ( j n e X LP filter Second Interpretation of the STFT
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3 ) ( n h k n j k e ) ( n x ) ( k j n e X BP filter n j k k k e n w n h ) ( ) ( where ) ( ) ( ) ( n h n x e e X k n j j n k k Bandpass Implementation ) ( 0 n h ) ( 1 n h N ) ( n x 1 0 )] ( * ) ( [ ) ( N k k n h n x n y ) ( * ) ( ) ( 1 0 N k k n h n x n y 1. Filterbank Summation Method (FBS)
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4 FBS Summary n j k j n k k k k k e e X n h n x n y n y ) ( )] ( * ) ( [ ) ( ) ( n j k k k e n w n h ) ( ) ( 1.
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