Marcio Guidorizzi de Siqueira

A unified framework for multichannel fast QRD-LS adaptive filters based on backward prediction errors

Fast QR decomposition algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Their application to multiple channel input signals generates more complex equations although the basic matrix expressions are similar. This paper presents a unified framework for a family of multichannel fast QRD-LS algorithms. This family comprises four algorithms - two basic algorithms with two different versions each. These algorithms are detailed in this work.

A new order recursive multiple order multichannel fast QRD-RLS algorithm

In many adaptive filtering applications, such as in the case of the Volterra filters, the use of channels of unequal orders is common. This paper introduces a new multichannel fast QRD-RLS algorithm based on the updating of a posteriori backward errors that attains both cases of channels of equal or unequal orders. This new algorithm exhibits good numerical behavior and is order recursive, which allows a systolic array implementation with lower computational complexity compared to earlier proposed algorithms.

Finite and Infinite-Precision Properties of QRD-RLS Algorithms

This chapter analyzes the finite and infinite-precision properties of QR-decomposition recursive least-squares (QRD-RLS) algorithms with emphasis on the conventional QRD-RLS and fast QRD-lattice (FQRD-lattice) formulations. The analysis encompasses deriving mean squared values of internal variables in steady-state and also the mean squared error of the deviations of the same variables assuming fixed-point arithmetic. In particular, analytical expressions for the excess of mean squared error and for the variance of the deviation in the tap coefficients of the QRD-RLS algorithm are derived, and the analysis is extended to the error signal of the FQRD-lattice algorithm. All the analytical results are confirmed to be accurate through computer simulations. Conclusions follow.

2 – Digital Filters

This chapter introduces the main steps for the design and implementation of linear and time-invariant digital filters. A digital filter is one of the basic building blocks in digital signal processing systems. Digital filtering consists of mapping a discrete-time sequence into another discrete-time sequence that highlights the desired information while reducing the importance of the undesired information. Digital filters are present in various digital signal processing applications related to speech, audio, image, video, and multi-rate processing systems. The widely available digital technology allows the implementation of very fast and sophisticated filters in a cheap and reliable manner. As a result, the digital fliers are found in numerous commercial products, such as audio systems, bio-medical equipment, digital radio, and TV. A typical digital signal processing (DSP) system comprises four types of modules: analog-to-digital (A/D) converter, digital filter, digital-to-analog (D/A) converter, and low-pass filter.