Audio Signal Processing and Coding

4.5 ANALYSIS-BY-SYNTHESIS LINEAR PREDICTION

In closed-loop source-system coders (Figure 4.7), the excitation source is determined by closed-loop or analysis-by-synthesis (A-by-S) optimization. The optimization process determines an excitation sequence that minimizes the perceptually weighted mean-square-error (MSE) between the input speech and reconstructed speech [Atal82b] [Sing84] [Schr85]. The closed-loop LP combines the spectral modeling properties of vocoders with the waveform matching attributes of waveform coders; and, hence, the A-by-S LP coders are also called hybrid LP coders. The system consists of a short-term LP synthesis filter, 1/A(z), and a LTP synthesis filter, 1/A_L(z), shown in Figure 4.7. The perceptual weighting filter (PWF), W(z), shapes the error such that quantization noise is masked by the high-energy formants. The PWF is given by

where γ₁ and γ₂ are the adaptive weights and L is the order of the linear predictor. Typically, γ₁ ranges from 0.94 to 0.98, and γ₂ varies between 0.4 and 0.7, depending upon the tilt or the flatness characteristics associated with the LPC spectral envelope [Sala98] [Bess02]. The role of W(z) is to de-emphasize the error energy in the formant regions [Schr79]. This de-emphasis strategy is based on the fact that quantization noise in the formant regions is partially masked by speech. From Figure 4.7, note that a gain factor, g, scales ...