LETI: Development of LETI Scientists Will Increase the Accuracy of Earthquake Prediction

In many applications that use modern methods and algorithms for digital signal processing, adaptive digital filters (ADF) are widely used, including a digital filter and an adaptation system. The most widely used ADFs are digital filters with a finite impulse response (FIR). Adaptive filtering is used in acoustic systems, image processing, equalizers designed to level the characteristics of communication channels, systems using adaptive antenna arrays.

The ADF efficiency is largely determined by the algorithm, which adapts the coefficients of the FIR filter to obtain the reference signal. At the same time, the algorithm, at a given step, must make adjustments with minimal software and hardware costs.

To increase the speed of signal processing in different applications, the use of a residue number system (RNS) is justified. The use of the RNS enables the enhancement of digital signal processing systems performance and reduces hardware costs due to the parallel and independent processing of small bit-width residues when performing arithmetic operations like addition, subtraction, and multiplication.

The disadvantage of the RNS is the high computational complexity when performing non-modular operations, which include division, sign detection, and numbers comparison. These limitations exist because the RNS is a non-positional number system, and numbers magnitude comparison in the RNS form is impossible, so the division operation consists of a magnitude comparison operation that is also problematic.

“Various scientists in different directions attempt to solve this problem, but there is still no universal solution suitable for any tasks. As a result, there are currently no coefficients adjustment algorithms for ADF that are implemented in the RNS. Therefore, the development of a new adaptation algorithm using the RNS and providing specified requirements to adaptation quality and rapidity is a critical task in digital signal processing.”

Dmitry Kaplun, Associate Professor of the Department of Automation and Control Processes
LETI scientists, together with their colleagues from North-Caucasus Federal University and Gauhati University (India), created a new algorithm for adjusting the coefficients of an ADF in an RNS. With its help, it is possible to solve the most important problem of digital signal processing. It will increase the signal processing rapidity at the expense of noise reduction without loss of quality. The study results were published in one of the most prestigious interdisciplinary journals, IEEE Access.

“To adjust each coefficient, it is necessary to perform one subtraction operation, one multiplication operation, and one addition operation modulo the RNS, so the recalculation time is proportional to the filter order. We provide a fundamentally new technique that surpasses the existing ones like LMS and RLS and their modifications in several parameters: adaptation (denoising) quality, ease of implementation, execution time, etc,” explained Dmitry Kaplun, “The main difference of 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.”

The scientists also proposed a procedure for developed algorithm applications depending on filter length and signal length. They performed mathematical modeling of the considered algorithms and demonstrated how the proposed technique can help the designer in the adjustment of the filter coefficients without extensive trial-and-error procedures. The researchers analyzed the denoising quality and computational complexity using synthetic and real earthquake recordings as examples.

The proposed algorithm can be useful for seismologists for better and faster determination of seismic activity, such as an earthquake or explosion; it will be in demand in hydroacoustics, bioinformatics, and other areas of human life.