The biorthonormal filter bank convolver, and application in low sensitivity FIR filter structures

It was shown by P.P. Vaidyanathan (1993) that in the case of orthonormal and biorthonormal filter banks one can convolve two signals x(n) and g(n) by directly convolving the subband signals and combining the results. In the present work, this result is further generalized. The coding gain for a biorthonormal convolver is also derived. As an application, a novel low-sensitivity FIR (finite impulse response) filter structure is derived from the convolution theorem. This FIR filter structure is shown to be attractive when the filter coefficients are quantized to low bit rate. For a fixed word length implementation, the deterministic coding gain over direct convolution for the cases of quantizing the input signal and filter coefficients is considered.<>