Digital filters with quantized coefficients : optimization and overflow analysis using extreme value theory
Abstract/Contents
- Abstract
- Parks-McClellan filter designs optimally minimize the maximum magnitude ripple in specific frequency bands for a given filter order. There are simple tools available for estimating the minimum order of a Parks-McClellan filter to meet a specific ripple requirement. However, many real-world filter implementations must first quantize filter coefficients, which can drastically reduce the performance of a Parks-McClellan design by increasing the maximum ripple. By making changes in the filter design specification within a very small range, a very large number of filter realizations with quantized coefficients can be generated. The problem is to choose the best design in the spirit of the original specification. For a Parks-McClellan specification, the best choice minimizes the peak of the ripple. Finding the best design out of perhaps millions of possibilities can be aided by making use of a statistical theory of extreme values. Extreme Value Theory is the study of the statistics of the maximum value or extreme outliers in a random process. We apply the theorems of Extreme Value Theory to the magnitude response of quantized filter designs with the goal of modeling the PDF of the maximum ripple in a particular frequency band. We find that the Generalized Extreme Value distribution, a fundamental distribution of Extreme Value Theory, well models the maximum ripple in quantized filters. This model can be used to estimate the filter order required to achieve a specific performance level for quantized Parks-McClellan designs. In addition, we present algorithms for generating fixed-point Parks-McClellan filters with improved performance, and compare the new algorithm to existing MATLAB tools. Secondly, we introduce a model for the distribution of extreme outliers at an arbitrary point within a digital system. Accurate estimates can be made of the probability that the signal is above a specific threshold, without knowledge of the exact PDF of the signal at that point. This model is useful for overflow analysis, as it can estimate the rate that a fixed-point signal will exceed its maximum representable value. Algorithms are presented and compared that can efficiently use this model on large datasets for automated overflow analysis.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Rowell, Adam Steven |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering |
| Primary advisor | Gill, John T III |
| Primary advisor | Widrow, Bernard, 1929- |
| Thesis advisor | Gill, John T III |
| Thesis advisor | Widrow, Bernard, 1929- |
| Thesis advisor | Schafer, Ronald W, 1938- |
| Advisor | Schafer, Ronald W, 1938- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Adam S. Rowell. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Adam Steven Rowell
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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