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Unformatted text preview: the er[n] is the quantization error of the residual: if the prediction of the signal is accurate then the variance of r[n] will be smaller than the variance of x[n] A quantizer with a given number of levels can be adjusted to give a smaller quantization error than would be possible when quantizing the signal directly. February 11, 2012 Veton Kpuska 67 Differential and Residual Quantization The differential coder of Figure 12.12 is referred to: Differential PCM (DPCM) when used with Adaptive Differential PCM (ADPCM) when used with a fixed predictor and fixed quantization. ADPCM yields greatest gains in SNR for a fixed bit rate. Adaptive prediction (i.e., adapting the predictor to local correlation) Adaptive quantization (i.e., adapting the quantizer to the local variance of r[n]) To achieve higher quality with lower rates it is required to: The international coding standard CCITT, G.721 with toll quality speech at 32 kbps (8000 samples/sec x 4 bits/sample) has been designed based on ADPCM techniques. Rely on speech modelbased techniques and The exploiting of longtime prediction, as well as Shorttime prediction February 11, 2012 Veton Kpuska 68 Differential and Residual Quantization Important variation of the differential quantization scheme of Figure 12.12. Prediction has assumed an allpole model (autoregressive model). In this model signal value is predicted from its past samples: Alternative approach is to use a finiteorder movingaverage predictor derived from the residual. One common approach of the use of the movingaverage predictor is illustrated in Figure 12.13 in the next slide. Any error in a codeword due to for example bit errors over a degraded channel propagate over considerable time during decoding. Such error propagation is severe when the signal values represent speech model parameters computed frameby frame (as opposed to samplebysample). February 11, 2012 Veton Kpuska 69 Differential and Residual Quantization February 11, 2012 Veton Kpuska 70 Differential and Residual Quantization Coder Stage of the system in Figure 12.13: Residual as the difference of the true value and the value predicted from the moving average of K quantized residuals: Decoder Stage: p[k] coefficients of P(z) ^ r[n] = a[n] - p[k ]r[n - k ]
k =1 K Predicted value is given by: Error propagation is thus limited to only K samples (or K analysis frames for the case of model parameters) ^ ^ ^ a[n] = r[n] - p[k ]r[n - k ]
k =1 K February 11, 2012 Veton Kpuska 71 Vector Quantization Vector Quantization (VQ) Investigation of scalar quantization techniques was the topic of previous sections. A generalization of scalar quantization referred to as vector quantization is investigated in this section. In vector quantization a block of scalars are coded as a vector rather than individually. An optimal quantization strategy can be derived based on a meansquared error distortion metric as with scalar quantization. February 11, 2012 Veton Kpuska 73 Vector Quantization (VQ) Motivation Assume the vocal tract transfer function is characterized by only two r...
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This note was uploaded on 02/10/2012 for the course ECE 3552 taught by Professor Staff during the Fall '10 term at FIT.
- Fall '10