By John G. Webster (Editor)
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Extra resources for 29.Information Theory
It has a stable histogram that can be approximated by a Laplacian distribution (31). With linear predictive coding, one can achieve a much higher SNR at a given bit rate. Equivalently, with linear predictive coding, one can reduce the bit rate for a given SNR. There are three basic components in the predictive coding encoder. They are predictor, quantizer, and coder, as illustrated in Fig. 16. As shown in Fig. 16, the predicted signal, xˆ[k], is subtracted from the input data, x[k]. The result of the subtraction is the prediction error, e[k], according to Eq.
With this presampling filter and a proper sampling rate, we can ensure that the spectral components of interest are within the bounds for which the signal can be recovered, as illustrated in Fig. 7. 2f1 – fh, 2f1, 2f1 + fh 3f1 – fh, 3 f1,3 f1 + fh f Figure 5. Spectrum of the sampled data sequence xs(t). Now, taking the Fourier transform of xs(t) in Eq. (5), the result is Xs ( f ) = +∞ −∞ 1 = T1 = 1 T1 1 T1 +∞ n=−∞ +∞ +∞ xa (t)e j2nπ f 1 t e − j2π f t dt n=−∞ +∞ −∞ xa (t)e− j2π ( f −n f 1 )t dt (6) Xa ( f − n f 1 ) n=−∞ QUANTIZATION We see from Eq.
Ideally the filter bank in the encoder would consist of a low-pass and a high-pass filter set with nonoverlapping, but contiguous, unit gain frequency responses. In reality the ideal filter is not realizable. Therefore, in order to convert the full spectrum, it is necessary to use filters with overlapping frequency response. As described earlier, the overlapping frequency response will cause aliasing. The problem is resolved by using exact reconstruction filters such as the quadrature mirror filters (QMF), as was suggested by Princey and Brad- xs[n] HPF ley (27), Croisier, Easteban, and Galand (28), Johnson (29), and Smith and Barnwell (30).
29.Information Theory by John G. Webster (Editor)