Arithmetic Fourier Transform And Adaptive Delta Modulation: A Symbiosis For High Speed Computation

D W Tufts; G Sadasiv

doi:10.1117/12.944048

20 April 1988 Arithmetic Fourier Transform And Adaptive Delta Modulation: A Symbiosis For High Speed Computation

D W Tufts, G Sadasiv

Proceedings Volume 0880, High Speed Computing; (1988) https://doi.org/10.1117/12.944048
Event: 1988 Los Angeles Symposium: O-E/LASE '88, 1988, Los Angeles, CA, United States

Abstract

We present preliminary results on the VLSI design and implementation of a novel and promising algorithm for accurate high-speed Fourier analysis and synthesis. The Arithmetic Fourier Transform (AFT) is based on the number -theoretic method of Mobius inversion. Its computations proceed in parallel and the individual operations are very simple. Except for a small number of scalings in one stage of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if ideal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Motivated by the goal of efficient, effective, high-speed realization of the algorithm in an integrated circuit, we introduce further simplicities by the use of delta modulation to represent the input function in digital form. The result is that only binary (or preferably, ternary) sequences need to be processed in the parallel computations. And the required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation (ADM).

Citation Download Citation

D W Tufts and G Sadasiv "Arithmetic Fourier Transform And Adaptive Delta Modulation: A Symbiosis For High Speed Computation", Proc. SPIE 0880, High Speed Computing, (20 April 1988); https://doi.org/10.1117/12.944048

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available