Special Issue on Mathematics and Digital Signal Processing

Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing; sonar, radar, and other sensor array processing; spectral density estimation; statistical signal processing; digital image processing; signal processing for telecommunications; control systems; and medical image analysis, among others.

This Special Issue has collected and now presents breakthrough research on the mathematical foundations and important applications of digital signal processing. Among the mathematical approaches to the development of new methods and tools for digital signal processing, special attention was paid to algebraic, number-theoretic, and statistical approaches. Among the applications of digital signal processing, the most relevant in this Issue were medicine, hydroacoustics, speech processing, and industrial production.

A total of ten research papers in various fields of mathematics and digital signal processing are presented in this Special Issue. Kaplun et al. [1] introduced a new approach for improving the calculation accuracy of digital filters based on finite field algebra. Pyko et al. [2] reported new approaches to digital signal processing for blood pressure monitoring. Chervyakov et al. [3] developed a new division algorithm in the residue number system, which is a promising alternative to the binary representation of information in digital signal processing. Lim [4] proposed a new sparse channel estimator, which is robust in impulsive noise environments. Another article by Chervyakov et al. [5] is devoted to the analysis of the quantization noise in discrete wavelet transform filters for three-dimensional medical imaging and the development of practical recommendations for the implementation of such systems in practice. A second article by Kaplun et al. [6] is devoted to the classification of hydroacoustic signals based on harmonic wavelets and a deep learning artificial intelligence system. The third article by Kaplun et al. [7] proposes an automated orientation algorithm based on the adjustment of the three-dimensional model virtual anatomical axis of the tibia, along with the vertical axis of the rectangular coordinates in three-dimensional space. Dehghan Firoozabadi et al. [8] reported the multiresolution speech enhancement based on a circular nested microphone array in combination with sub-band affine projection algorithm. Klishkovskaia et al. [9] wrote about the development of classification algorithms for the detection of postures using non-marker-based motion capture systems. Yang et al. [10] combined a deep learning feature extraction method and an extreme learning machine classification method to create an extreme depth learning machine model for detecting wood image defects.

Although submissions for this Special Issue have been closed, more in-depth research in mathematics and digital signal processing continues to address the challenges we face today, such as improving the performance and quality of digital signal processing systems, developing artificial intelligence methods for digital signal processing, and developing fundamentally new software and hardware solutions for solving applied problems of digital signal processing.