Error Properties of Hartley Transform Algorithms.

Abstract

In this thesis, the error properties of various discrete Hartley transform (DHT) algorithms are investigated theoretically and experimentally. More specifically, the author analyzes the arithmetic roundoff error characteristics of DHT algorithms proposed by Bracewell and Wang and develops and analyzes a new DHT algorithm. Statistical models for roundoff errors and linear system noise theory are employed to estimate output noise variance for these DHT algorithms. By considering the overflow constraint in conjunction with these noise analyses, output noise to signal ratios are derived for both fixed and floating-point arithmetic. Experiments are used to support the theoretical predictions obtained via the statistical models. The empirical results are found to be in excellent agreement with the predictions based on the models. Comparing Bracewell's, Wang's and the new algorithm in terms of their error properties, it is found that Bracewell's algorithm exhibits the most desirable error characteristics. These results were found to hold for both decimation-in-time and frequency and for a variety of different radices. For a given radix, the total operation count for all algorithms investigated in this thesis are found to be identical. Keywords: electrical engineering; signal processing. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA163217

Entities

People

  • Avideh Zakhor

Organizations

  • Massachusetts Institute of Technology

Tags

DTIC Thesaurus Topics

  • Agreements
  • Algorithms
  • Arithmetic
  • Electrical Engineering
  • Engineering
  • Floating Point Operations
  • Frequency
  • Information Theory
  • Linear Systems
  • Signal Processing

Fields of Study

  • Engineering

Readers

  • Approximation Theory.
  • Computational Modeling and Simulation
  • Computer Programming and Software Development.