Modeling and analysis of floating point quantization errors in subband filter structures

摘要

This paper is concerned with the analysis and modeling of the effects of floating point quantization of subband signals in a two channel filter bank. It represents an extension of previous work for optimal fixed-point quantizers. In the present case, the quantization noise is modeled by a multiplicative noise as compared with additive noise representation for the fixed- point case. We derive equations for the autocorrelation and power spectral density (PSD) of the reconstructed signal y(n) in terms of the analysis/synthesis filters, the PSD of the input, and the quantizer model. Formulas for the mean-square error and for compaction gain are obtained in terms of these parameters. We assume the filter bank is perfect reconstruction (PR) (but not necessarily paraunitary) in the absence of quantization and transmission errors. The autocorrelation function of the output y(n) is generally non-stationary. However, it is cyclostationary since it is stationary when n is odd, or n is even; but not both. By taking the average of the autocorrelation for n even, and for n odd, we obtain a stationary autocorrelation, and its associated PSD. This cyclostationary analysis is used to compute the quantization noise component in the output, for any PR subband structure.