Optimal biorthogonal filter banks with minimization of quantization noise amplification

In this work we find out the optimal biorthogonal filter bank, in the ideal case, employing the proposed minimization of quantization noise amplification. In the ideal case it turns out to be a paraunitary filter bank which completely decorrelates the input signal, followed by scalar DPCM on each of the subbands. Its coding gain is shown to be equal to that of the ideal scalar DPCM coder acting on the original signal, irrespective of the number of channels. But the previously known optimal biorthogonal filter bank attains this coding gain only when the number of channels tends to infinity. The coding gain advantage of the new optimal filter bank structure, in the FIR case, is verified. The minimization of quantization noise amplification is also used to maximize the coding gain of a given biorthogonal filter bank. The coding gain improvements are verified for low bit-rates by measuring the reconstruction error introduced in coding an AR(1) source.