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