Application of matrix in signal processing

Abstract

Signal processing, a foundational discipline in modern technology, encompasses a diverse array of applications, ranging from audio and image processing to communication systems and medical imaging. This review investigates how matrix-based techniques are widely used to advance signal processing methodologies. In order to discretize continuous-time signals for digital processing, which occurs in the first section of the paper, matrices play a crucial role in signal sampling. A key principle, the Nyquist-Shannon Sampling Theorem, directs appropriate sampling rates to prevent aliasing, with matrices permitting effective signal representation. The effectiveness of matrix-based filtering methods for frequency modulation and noise reduction, such as convolution and correlation, is then investigated. By utilising matrix operations, these methods enable real-time signal processing. The Fourier Transform and Wavelet Transform are also featured in matrix-driven signal transformation, providing insights into frequency analysis and non-stationary signal characterization. By reducing noise components, matrix-based approaches, particularly Singular Value Decomposition (SVD) denoising, are essential for improving signal quality. Additionally, image compression employs SVD. Matrix-based compressive sensing revolutionises signal recovery from sparse data and results in data-efficient reconstruction. Signal processing has been transformed by matrix-based approaches, which have enabled previously unheard-of levels of efficiency, accuracy, and adaptability. The review highlights their significant influence on several signal processing fields.