Amplitude Bounds and Quantization Schemes in Walsh-Fourier Domain

Abstract

Discrete Walsh-Fourier transform (WET) have found increasing use in the area of digital signal processing and transmissicon. Assuming that the signal is amplitude-bounded, bounds on the WFT domain sample amplitudes are obtained. From an appropriately chosen group of sample amplitudes in the WET domain, corresponding set of mutually exclusive and exhaustive subsums in the signal damain can be obtained. From the knowledge of these subsums, amplitude bounds on the remaining WET domain samples can be obtained. The group of sample amplitudes in the WFT domain may be recursively chosen. This results into the partitioning of WET domain in various sets such that all the samples of a particular set have the same amplitude bounds. Two such recursive procedures are worked out. Set-dependent quantization transfer characteristics, restricteci within the dynamic amplitude range appropriate to individual sets, are proposed. Effect of both the set-dependent WFT damain quantization schemes on the reconstructed signal is analyzed. Efficient computational algorithms are developed. Appropriate signal characteristics for both the schemes are pointed out.