Publications

In this paper, we develop iterative algorithms for reconstructing a minimum phase sequence from pthhea se or magnitude of its Fourier transform. These iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain. This approach is the basis of a new means of computing the Hilbert transform of the log-magnitude or phase of the Fourier transform of a minimum phase sequence which does not require phase unwrapping. Finally, we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence.

When digital signal processing operations are implemented on a computer or with special-purpose hardware, errors and constraints due to finite word length are unavoidable. The main categories of finite register length effects are errors due to A/D conversion, errors due to roundoffs in the arithmetic, constraints on signal levels imposed by the need to prevent overflow, and quantization of system coefficients. The effects of finite register length on implementations of linear recursive difference equation digital filters, and the fast Fourier transform (FFT), are discussed in some detail. For these algorithms, the differing quantization effects of fixed point, floating point, and block floating point arithmetic are examined and compared. The paper is intended primarily as a tutorial review of a subject which has received considerable attention over the past few years. The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff. The analyses presented here are intended to illustrate techniques of working with particular models. Results of previous work are discussed and summarized when appropriate. Some examples are presented to indicate how the results developed for simple digital filters and the FFT can be applied to the analysis of more complicated systems which use these algorithms as building blocks.

Application of a type of predictive coding to the channel signals of a homomorphic vocoder has produced sizable bit rate reductions. With only slight degradation in speech quality, reduction (for the spectral envelope information) from 7800 to 4000 bits/s was achieved. A technique for obtaining the formant frequencies from the predictive coding parameters is described; this approach promises further bit rate reductions. As a byproduct of this study of predictive coding, direct and cascade form speech synthesizers are compared on the basis of differing quantization effects.

A statistical model for roundoff noise in floating point digital filters, proposed by Kanoko and Liu, is tested experimentally for first- and second-order digital filters. Good agreement between theory and experiment is obtained. The model is used to specify a comparison between floating point and fixed point digital filter realizations on the basis of their output noise-to-signal ratio, and curves representing this comparison are presented. One can find values of the filter parameters at which the fixed and the floating point curves will cross, for equal total register lengths.