# Lecture12 - Lecture 12 EE214A Abeer Alwan Some Applications...

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1 Lecture 12 EE214A Abeer Alwan Some Applications LPC10 speech coder The SIFT algorithm

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2 Application Example: Pitch-Excited LPC Transmitter Block Diagram of a Pitch-Excited LPC Receiver
3 Direct Form Implementation of the Vocal Tract Filter Speech Coding Linear Prediction A ( z ) s ( n ) + d ( n ) s e ( n ) d ( n ) A ( z ) + + s e ( n ) s r ( n ) Try to predict the current sample value; Could also transmit the prediction error .

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4 Application Example II: The SIFT Algorithm for Pitch Detection Typical Signals from the SIFT Algorithm
5 2. Covariance method 1 0 ( , ) ( ) ( ) ( , ) N n i k s n i s n k k i n k n k i n s k n s a i n s n s ) ( ) ( ) ( ) ( p k k k i a i i 1 ) , ( ) , 0 ( ) 0 , ( p k k k a E 1 min ) , 0 ( ) 0 , 0 ( Recall: Then, Also, The method requires samples from -p to N-1 2 min ( ) ( ) ( ) k n k n E s n a s n s n k Define and Matrix notation ) 0 , ( ) 0 , 2 ( ) 0 , 1 ( ) , ( ) 1 , ( ) 2 , 2 ( ) 1 , 2 ( ) , 1 ( ) 2 , 1 ( ) 1 , 1 ( 2 1 p a a a p p p p p 1 a a   is symmetric but not Toeplitz (not diagonal)

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6 AC vs. Covariance Example: Compare the AC and covariance methods for a 1 st -order system.
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• Winter '11
• ALWAN
• Gaussian Elimination, linear prediction, Toeplitz, Toeplitz matrix, Levinson recursion, Levinson-Durbin Recursion

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