Probability, random processes, and estimation theory for engineers
Probability, random processes, and estimation theory for engineers
Fast fourier transforms: a tutorial review and a state of the art
Signal Processing
DFT/FFT and Convolution Algorithms: Theory and Implementation
DFT/FFT and Convolution Algorithms: Theory and Implementation
A theory of nonsubtractive dither
IEEE Transactions on Signal Processing
Exact recovery of higher order moments
IEEE Transactions on Information Theory
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Fourier transform is undoubtedly one of the cornerstones of digital signal processing (DSP). The introduction of the now famous FFT algorithm has not only breathed a new lease of life into an otherwise latent classical DFT algorithm, but also led to an explosion in applications that have now far transcended the confines of the DSP field. For a good accuracy, the digital implementation of the FFT requires that the input and/or the 2 basis functions be finely quantized. This paper exploits the use of coarse quantization of simplifying its architecture. In order to resolve this apparent conflict between preserving an excellent computational accuracy while using a quantization scheme as coarse as can be desired, this paper advances new theoretical results which form the basis for two new and practically attractive FFT estimators that rely on the principle of 1 bit nonsubtractive dithered quantization (NSDQ). The proposed theory is very well substantiated by the extensive simulation work carried out in both noise-free and noisy environments. This makes the prospect of implementing the 2 proposed 1 bit FFT estimators on a chip both practically attractive and rewarding and certainly worthy of a further pursuit.