Plot the Filter Bank of a Discrete Wavelet in Python
Filters method is an efficient way to implement Discrete Wavelet Transform
1. Wavelet Filter Bank
In practice, an efficient way to implement Discrete Wavelet Transform (DWT) is to use filters method, which was developed in 1988 by Mallat. This very practical filtering algorithm yields a Fast Discrete Wavelet Transform (FWT).
2. Wavelet filters coefficients
Wavelet filters coefficients are the most important information used in Discrete Wavelet Transforms (DWT). In the PyWavelets library of Python, filters coefficients can be obtained via the dec_lo, dec_hi, rec_lo and rec_hi attributes, which correspond to lowpass and highpass decomposition filters and lowpass and highpass reconstruction filters respectively.
In a previous article, we have already learned what PyWavelets is, how to install it, and how to display its built-in Wavelets families and their members in PyWavelets, and so on. In the PyWavelets, the filter_bankmethod returns a list for the current wavelet in the following order: [dec_lo, dec_hi, rec_lo, rec_hi].
dec_lo: Decomposition low-pass filterdec_hi: Decomposition high-pass filterrec_lo: Reconstruction low-pass filter
