Abstract
The paper discusses adaptive filtering using Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. An algorithm for adjusting the coefficients of an adaptive digital filter in the Residue Number System and a procedure of developed algorithm applying depending on filter length and signal length are proposed. Mathematical modeling of the considered algorithms is performed. Examples are presented to demonstrate how the proposed technique can help the designer in the adjustment of the filter coefficients without the need for extensive trial-and-error procedures. The analysis of the denoising quality and computational complexity is made. Synthetic and real data (earthquake recording) were used while testing. The proposed algorithm surpasses the existing ones like LMS and RLS, and their modifications in a number of parameters: adaptation (denoising) quality, ease of implementation, execution time. The main difference between the developed algorithm is the sequential adaptation of each coefficient with zero error. In the known algorithms, the entire vector of coefficients is iteratively adapted, with some specified accuracy. The iterations (steps) number is determined by the input signal length for all algorithms.
Highlights
Using adaptive digital signal processing (DSP) techniques in modern communication systems, the enhancement of the primary quality functioning indicators [1], [2] is achieved.This is especially evident with the digital filtering of processed signals
Since we have extended the work into residue number system (RNS), for this we will have to produce the reverse conversion of the RNS-binary number system (BNS), do a comparison, and if the required error is not achieved, generate further coefficients’ adaptation
In [32], a hybrid Residue Number System (RNS) implementation of an adaptive finite impulse response (FIR) filter based on the Least Mean Square (LMS) adaptation algorithm is presented
Summary
Using adaptive digital signal processing (DSP) techniques in modern communication systems, the enhancement of the primary quality functioning indicators [1], [2] is achieved. The development of a new adaptation algorithm (filter coefficients adjustment) using the RNS and providing specified requirements to adaptation quality and rapidity indicators is a critical task in digital signal processing. Given the advantages and disadvantages of the considered adaptation algorithms, we can conclude that RNS is suitable to improve performance when adjusting the coefficients and reduce the computational complexity of the tuning procedure [22]. These results can be used for building effective parallel computational systems [13] based on computers with parallel structure like FPGA [17], [18] and GPU [23], [24].
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