{"id":7554,"date":"2022-04-25T00:00:00","date_gmt":"2022-04-25T00:00:00","guid":{"rendered":"https:\/\/academy.deepsim.caplot-the-filter-bank-of-a-disctete-wavelet-in-python-42fbb6eb418d\/"},"modified":"2022-11-25T04:03:58","modified_gmt":"2022-11-25T04:03:58","slug":"plot-the-filter-bank-of-a-disctete-wavelet-in-python-42fbb6eb418d","status":"publish","type":"post","link":"https:\/\/academy.deepsim.ca\/zh\/plot-the-filter-bank-of-a-disctete-wavelet-in-python-42fbb6eb418d\/","title":{"rendered":"\u4f7f\u7528Python\u7ed8\u5236\u79bb\u6563\u5c0f\u6ce2\u6ee4\u6ce2\u5668\u7ec4\u7684\u56fe\u50cf"},"content":{"rendered":"

Filters method is an efficient way to implement Discrete Wavelet Transform<\/p>\n

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1. What is a Filter Bank<\/h3>\n

Filter banks play an important role in modern signal and image processing. As its name suggests, a Filter Bank is a bank of filters, meaning a collection of filters, or many filters in simple words, and each of the filter is applied to the original signal. So, one signals can be decomposed into 2 or more signals out. Then what is a Filter bank?<\/p>\n

Simply speaking, a Filter Bank can be defined as a system (an array) of bandpass filters\u00a0\u00a0that split the input signal (S<\/i><\/em>t<\/i><\/sub><\/em>) into a set of analysis signals (x<\/i><\/em>1t<\/sub>, x<\/i><\/em>2t<\/sub>, \u2026, x<\/i><\/em>nt<\/sub> ) and each one carrying a single frequency sub-band of the original signal.<\/p>\n\n

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Fig. 1. Structure of a Filter Bank<\/strong><\/figcaption><\/figure>\n<\/div>\n\n\n

In wavelet analysis, filter banks usually refers to a class of systems that generates scaling and wavelet function. The below figure shows the simple structure of a filter bank can be illustrated by the figure below.<\/p>\n\n\n\n

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).<\/p>\n\n\n\n

2. Wavelet filters coefficients<\/h3>\n\n\n\n

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<\/strong>, dec_hi<\/strong>, rec_lo<\/strong> and rec_hi<\/strong> attributes, which correspond to lowpass<\/em> and highpass<\/em> decomposition filters<\/strong> and lowpass<\/em> and highpass<\/em> reconstruction filters<\/strong> respectively.<\/p>\n\n\n\n

In a previous article<\/a>, 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_bank<\/code>method returns a list for the current wavelet in the following order: [dec_lo, dec_hi, rec_lo, rec_hi].<\/code><\/p>\n\n\n\n