Application of functional analysis in signal processing

Abstract

This paper presents the application of linear generalization in the field of digital signal processing. Digital signal processing, as a common signal processing method, requires the digital conversion of analog signals. In order to better process digital signals, mathematical tools such as matrix operations must be used. This is where linear generalization becomes particularly important. A linear general function is a linear mapping from a vector space to a corresponding pure volume domain and can be expressed as the action of a column vector on a vector. The processing of linear general functions enables the finer handling of digital signals, facilitating the filtering out of noise and interference, and thus the generation of higher-quality signals. Furthermore, the linear general function is employed in a variety of signal recognition, feature extraction, peak detection and other applications, providing a robust theoretical foundation for digital signal processing.