An application-specific architecture for the parallel calculation of the decimation in time and radix 2 fast Hartley (FHT) and Fourier (FFT) transforms is presented. A real sequence with N=2/sup n/ data items is considered as input. The system calculates the FHT and the FFT in n and n+1 stages. respectively. The modular and regular parallel architecture is based on a constant geometry algorithm using butterflies of four data items and the perfect unshuffle permutation. With this permutation, the mapping of the algorithm in VLSI technology is simplified and the communications among processors are minimized. Organization of the processor memory based on first-in, first-out (FIFO) queues facilitates a systolic data flow and permits the implementation in a direct way of the complex data movements and address sequences of the transforms. This is accomplished by means of simple multiplexing operations, using hardwired control. The total calculation time is (Nlog/sub 2/N)/4Q cycles for the FHT and N(1+log/sub 2/N)/4Q cycles for the FFT, where Q is the number of processors (Q= 2/sup q/, Q >

A VLSI constant geometry architecture for the fast Hartley and Fourier transforms

In this paper, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 2 pi discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This paper compares existing algorithms for computing the unwrapped phase. Then, two composite algorithms are proposed that build upon the existing ones. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.

/pdf/computation-of-the-one-dimensional-unwrapped-phase-4x913gqua5.pdf

Computation of the One-Dimensional Unwrapped Phase

The real cepstrum is used to design an arbitrary length minimum-phase finite-impulse response filter from a mixed-phase prototype. There is no need to start with the odd-length equiripple linear-phase filter first. Neither the phase-unwrapping nor root-finding procedure is needed. Only two fast Fourier transforms and a recursive procedure are required to find the filter's impulse response from its real cepstrum. The resulting filter's magnitude response is exactly the same as the original one even when the filter is of very high order

/pdf/minimum-phase-fir-filter-design-using-real-cepstrum-143s2ru75f.pdf

Minimum-Phase FIR Filter Design Using Real Cepstrum

The real cepstrum is used to design an arbitrary length minimum-phase FIR filter from a mixed-phase sequence. There is no need to start with the odd-length equiripple linear-phase sequence first. Neither phase-unwrapping nor root-finding is needed. Only two FFTs and an iterative procedure are required to compute the filter impulse response from real cepstrum; the resulting magnitude response is exactly the same with the original sequence.

Minimum-phase FIR filter design using real cepstrum

Improved Wigner-Ville distribution performance by signal decomposition and modified group delay

The use of the Hartley transform (HT) in cepstrum analysis, as a substitute for the more commonly used Fourier transform (FT), is examined. With this substitution, the input to the cepstrum must be in the real domain only. The benefits of using the HT are approximately 50% less data memory required and approximately 40% faster program execution, at no loss in accuracy. >

M.C. Steckner

Papers

Fast cepstrum analysis using the Hartley transform