Comparative Analysis of Digital FIR Filter using Various Types of Modular Arithmetic Algorithms

Number theory algorithms are extensively required for many digital signal processing (DSP) systems. Over the last few decades, the science community has been discovering the practical applications of number theory. High-speed number manipulation for arithmetic operations is a key component in DSP applications.For that alternative arithmetic hardware may find a niche. This work consists of designing FIR filter using Residue number system and Logarithmic number system. Also, proposed novel RLNS scheme based on the merging of RNS and LNS. Compared to other number systems, the Residue Logarithmic Number System (RLNS) offers faster operation and more precision. Our prior work explains the creation of the Fixed-width multiplier utilizing the RLNS multiplier as well as the performance evaluation. Because of its distinct area and power compactness qualities, the fixed-width multiplier has been deployed.Though the Fixed-width multiplier has its attractive characteristics, it has a limitation of producing truncation error. Additionally, the truncation error was effectively decreased by 89% using the Taylor series expansion for the error approximation, which is significantly less than the orthodox truncated multiplier. The expansion of the earlier work is presented in this paper. The digital FIR filter uses a fixed-width multiplier that is based on RLNS architecture.Then the implemented FIR filter can be used for many image or video processing applications. The filter co-efficient has been processed via Fast Fourier Transform (FFT) considered a complicated algorithm for complex numbers. Finally, the comparative analysis of designed filter using RNS, LNS and RLNS has performed. From the investigation, we conclude that the proposed novel RLNS algorithm provides high performance for DSP applications.The parameter signal-to-noise (SNR) ratio is very significant to measure the value of the precision of the proposed filter. If the SNR value is higher than 25 dB, the filter performs well. Additionally, we achieved a 35 dB SNR ratio in this work. With MATLAB software, the anticipated output response of the filter design has been modeled.