1D Multilevel Discrete Wavelet Transform (1): Decomposition Method

Methods on how to decompose 1D signal into approximation and detail coefficients at multilevel with Discrete Wavelet Transform (DWT)

The series of 1D multilevel discrete wavelet transform methods includes 3 parts:

Part I: Decomposition Method

Part II: Reconstruction Method

Part III: Partial Reconstruction Methods

In the last few articles, we have learned how to make 1D single level, or called 1 stage, Discrete wavelet transform (DWT). One stage DWT is the simplest and fundamental of DWT, which is very helpful when your data is not high frequency (HF).

However, the frequency of the signals in our daily life is usually very high, and thus we need multilevel DWT to analyze these signals with high frequency. From this article, we will investigate how to make multilevel DWT on 1D signals, and this article focuses on DWT decomposition method.

Summary

This article shows how to decompose a 1D signal into approximation and detail coefficients at multilevel with Discrete Wavelet Transform (DWT) using PyWavelets library. It mainly presents three essential topics: (1) multilevel discrete wavelet decomposition method in PyWavelets, (2) methods to calculate coefficients lengths at the different levels, and (3) method to calculate maximum decomposition levels of Discrete wavelet transform.

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