Research and Analysis of One-dimensional Discrete Wavelet Transform

Authors:
Publisher website
Google Scholar
Abstract
In the digital information age, signal processing technology has become an increasingly popular research direction. Among them, discrete wavelet transform, which is widely used in signal analysis, image compression, and video coding, is an important research topic. In the process of multi-resolution analysis, each layer of decomposition causes the signal to pass through a low-pass filter and a band-pass filter, and the signal is decomposed into a low-frequency part and a high-frequency part. The characteristics of the low-pass filter are determined by the scaling function φ(x), and the characteristics of the band-pass filter are determined by the wavelet function ψ(x). The decomposed coefficient consists of two parts: low frequency coefficient vector cA and high frequency coefficient vector cD. The low frequency coefficient vector cA is obtained by convolution of the impulse response of the signal and the low-pass filter, which reflects the low frequency component of the signal. High-frequency coefficient vector cD is obtained by convolution of signal and bandpass filter, which reflects the high frequency component of signal.

This publication has 3 references indexed in Scilit: