diff quntn

diff quntn - Differential PCM Lecture Notes &...

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Unformatted text preview: Differential PCM Lecture Notes & Examples John Leis April 3, 2006 1 Differential Quantization PCM = pulse-code modulation. Used to describe simple A/D conversion. DPCM = differential PCM, ie take the difference and transmit that. Since the differences is smaller, one of the previous quantization methods may be used with fewer bits and/or better quality. A model for a signal is s ( n ) = ˆ s ( n ) + e ( n ) (1) where s ( n ) is the signal sample at instant n , ˆ s ( n ) is an estimation (or approximation) of the signal, and e ( n ) is an error term dependent on the accuracy of the model. The ˆ s ( n ) term may be viewed as the deterministic component, with the error e ( n ) the stochastic component. The deterministic component is uniquely described by the model parameters, whilst the stochastic component is described in statistical terms. A model which gives good performance ( σ 2 e σ 2 s ) for voiced speech segments is a weighted linear sum ˆ s ( n ) = a 1 s ( n- 1) + a 2 s ( n- 2) + ··· + a p s ( n- P ) (2) = P X k =1 a k s ( n- k ) (3) Equation 3 is known to give good prediction for so-called “voiced” sections of speech, where the vocal cords vibrate at a fixed rate. Less accurate modelling is obtained for unvoiced and transitory regions of speech. note: matlab uses -a(k) in the above, and stores coefficients in vector A = [1 a(1) ... a(p)]’ Combining and re-arranging the above equations gives: e ( n ) = s ( n )- ˆ s ( n ) z }| { P X k =1 a k s ( n- k ) (4) however, the decoder does not know e precisely due to quantization (rounding or approximation), and hence the signal s ( n ) is not known precisely at the decoder. 1 s ( n ) ∑ +- Q ( · ) e ( n ) ˆ e ( n ) ∑ + + 1- A ( z ) ˆ s ( n ) ˜ s ( n ) ˜ s ( n ) Figure 1: A differential PCM (DPCM) encoder. The prediction is based upon the quantized prediction error ˆ e ( n ) together with past predictions ˜ s ( n ). ˆ e ( n ) ∑ + + ˆ s ( n ) ˜ s ( n ) 1- A ( z ) Figure 2: A differential PCM (DPCM) decoder. The prediction (based on past quantized outputs) is added to the received error signal ˆ e ( n ) to generate each output ˆ s ( n )....
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diff quntn - Differential PCM Lecture Notes &...

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