Statistical Analysis of Digital Fixed-Point Multiplication Errors and Quantization Errors

摘要

The problem considered is to review and extend the theory of computation error generation in digital filters. Specifically, consider fixed-point multiplication for digitized Gaussian analog signal inputs. Deterministic properties of rounding and chopping were examined for both multiplication and quantization errors. Statistical properties of rounding only were examined for both multiplication and quantization errors. Statistical properties examined are (1) the error distribution density, (2) the error variance, (3) the autocorrelation between successive error values, and (4) the cross-correlation coefficient between the quantizer input and the resulting error. Specific results were obtained for zero-mean Gaussian random processes. (Author)