This book describes how a key signal/image processing algorithm - that of the fast Hartley transform (FHT) or, via a simple conversion routine between their outputs, of the real-data version of the ubiquitous fast Fourier transform (FFT) - might best be formulated to facilitate computationally-efficient solutions. The author discusses this for both 1-D (such as required, for example, for the spectrum analysis of audio signals) and m-D (such as required, for example, for the compression of noisy 2-D images or the watermarking of 3-D video signals) cases, but requiring few computing resources (i.e. low arithmetic/memory/power requirements, etc.). This is particularly relevant for those application areas, such as mobile communications, where the available silicon resources (as well as the battery-life) are expected to be limited. The aim of this monograph, where silicon-based computing technology and a resource-constrained environment is assumed and the data is real-valued innature, has thus been to seek solutions that best match the actual problem needing to be solved.

Autorentext

Dr. Keith John Jones received his Ph.D in Computer Science from Birkbeck College, London University and his M.Sc in Applicable Mathematics from Cranfield Institute of Technology. He has an entry in Who's Who in Science and Engineering (2008-present) and in The Dictionary of International Biography (otherwise known as The Cambridge Blue Book) (2008-present). He is currently a consultant at Wyke Technologies Ltd., Weymouth, Dorset (2015-present), having previously been employed as a mathematician/algorithmist/programmer & system designer for TRL Technology Ltd., Tewkesbury, Gloucestershire and, prior to that, for QinetiQ, Winfrith, Dorset. In 2010 he published The Regularized Fast Hartley Transform: Optimal Formulation of Real-Data Fast Fourier Transform for SiliconBased Implementation in Resource-Constrained Environments. He has 10 patents and has published extensively in the field.

Klappentext

This book describes how a key signal/image processing algorithm that of the fast Hartley transform (FHT) or, via a simple conversion routine between their outputs, of the realdata version of the ubiquitous fast Fourier transform (FFT) might best be formulated to facilitate computationally-efficient solutions. The author discusses this for both 1-D (such as required, for example, for the spectrum analysis of audio signals) and mD (such as required, for example, for the compression of noisy 2-D images or the watermarking of 3-D video signals) cases, but requiring few computing resources (i.e. low arithmetic/memory/power requirements, etc.). This is particularly relevant for those application areas, such as mobile communications, where the available silicon resources (as well as the battery-life) are expected to be limited. The aim of this monograph, where siliconbased computing technology and a resourceconstrained environment is assumed and the data is real-valued in nature, has thus been to seek solutions that best match the actual problem needing to be solved.

Zusammenfassung
Most real-world spectrum analysis problems involve the computation of the real-data discrete Fourier transform (DFT), a unitary transform that maps elements N of the linear space of real-valued N-tuples, R , to elements of its complex-valued N counterpart, C , and when carried out in hardware it is conventionally achieved via a real-from-complex strategy using a complex-data version of the fast Fourier transform (FFT), the generic name given to the class of fast algorithms used for the ef?cient computation of the DFT. Such algorithms are typically derived by explo- ing the property of symmetry, whether it exists just in the transform kernel or, in certain circumstances, in the input data and/or output data as well. In order to make effective use of a complex-data FFT, however, via the chosen real-from-complex N strategy, the input data to the DFT must ?rst be converted from elements of R to N elements of C . The reason for choosing the computational domain of real-data problems such N N as this to be C , rather than R , is due in part to the fact that computing equ- ment manufacturers have invested so heavily in producing digital signal processing (DSP) devices built around the design of the complex-data fast multiplier and accumulator (MAC), an arithmetic unit ideally suited to the implementation of the complex-data radix-2 butter?y, the computational unit used by the familiar class of recursive radix-2 FFT algorithms.

Inhalt
Part 1: The Discrete Fourier and Hartley Transforms.- Background to Research.- The Real-Data Discrete Fourier Transform.- The Discrete Hartley Transform.- Part 2: The Regularized Fast Hartley Transform.- Derivation of Regularized Formulation of Fast Hartley Transform.- Design Strategy for Silicon-Based Implementation of Regularized Fast Hartley Transform.- Architecture for Silicon-Based Implementation of Regularized Fast Hartley Transform.- Design of CORDIC-Based Processing Element for Regularized Fast Hartley Transform.- Part 3: Applications of Regularized Fast Hartley Transform.- Derivation of Radix-2 Real-Data Fast Fourier Transform Algorithms using Regularized Fast Hartley Transform.- Computation of Common DSP-Based Functions using Regularized Fast Hartley Transform .- Part 4: The Multi-Dimensional Discrete Hartley Transform.- Parallel Reordering and Transfer of Data between Partitioned Memories of Discrete Hartley Transform for 1-D and m-D Cases.- Architectures for Silicon-Based Implementation of m-D Discrete Hartley Transform using Regularized Fast Hartley Transform.- Part 5: Results of Research.- Summary and Conclusions.