Analysis of fixed-point digital filters using Markov chains.

Author(s)

Fernando Gonçalves de Almeida Neto

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2011-02-18

Examining board members

Vítor Heloiz Nascimento; Miguel Arjona Ramírez; Leonardo Tomazeli Duarte

• Advisor: Vítor Heloiz Nascimento

Abstract

The implementation cost of signal processing algorithms may be reduced by using fixed-point arithmetic with the smallest possible word-length for each variable or parameter. This allows the designer to reduce hardware complexity, leading to economy of energy and chip area in dedicated circuits. The choice of word-length depends on the determination of the effect at the output of the quantization of each variable, which may be obtained through simulations (generally slow) or through analytical methods. This document proposes new advances to a new analysis method for digital signal processing algorithms implemented in fixed-point arithmetic, based on Markov chain models. Our contributions are the following: A Markov chain model is used to study first and second order IIR filters for an known input density probability function. The model is general and can be applied for any probability function. We use the output of the filters to define the states of the Markov chain. The unidimensional LMS Markov chain model is extended to correlated input. The states are defined by a pair considering the coefficient and the previous input and an example assuming Gaussian-distributed input is presented. (AU)

• FAPESP's process: 09/03609-0 - Analysis of fixed-point digital filters using Markov chains
• Grantee: Fernando Gonçalves de Almeida Neto
• Support Opportunities: Scholarships in Brazil - Master