Basic Concepts of Wavelets Transform

Learning Wavelet Transform should start from basic concepts

I published three posts at the very beginning when I joined medium, which are about visualization of wavelet function and scaling function, visualization of filter bank of a Discrete Wavelet and applications of wavelet transform.

From this post, I will continue to write some practical tutorial articles on how to apply Wavelet Transform to solve real-world problems. It is better to know some basic concepts related with Wavelet Transform (WT) before using it for real-world cases.

1. What is a Wavelet?

A wavelet is a wave-like oscillation, which is a “brief oscillation” or “small oscillation”. Its amplitude begins at zero, increases or decreases, and then returns to zero one or more times. Let’s see some wavelets plots as follows:

2. Wavelet Transform

In the signal processing context, Wavelet transform (WT), also called wavelet analysis, is a method to decompose an input signal of interest into a set of elementary waveforms, i.e. “wavelets”