68 lines
2.2 KiB
Markdown
68 lines
2.2 KiB
Markdown
# [PyWavelets](https://pywavelets.readthedocs.io/en/latest/) -- Wavelet Transforms in Python
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## The goal
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How do we do wavelet transforms under Python?
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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You might want to read: [A Practical Guide to Wavelet Analysis](https://paos.colorado.edu/research/wavelets/) -> [PDF](https://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf)
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```shell
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pip install PyWavelets
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```
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## Which [continuous mother wavelets](https://pywavelets.readthedocs.io/en/latest/ref/cwt.html#continuous-wavelet-families) are available?
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```python
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import pywt
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wavelet_list = pywt.wavelist(kind="continuous")
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print(wavelet_list)
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```
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```Python console
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['cgau1', 'cgau2', 'cgau3', 'cgau4', 'cgau5', 'cgau6', 'cgau7', 'cgau8', 'cmor', 'fbsp', 'gaus1', 'gaus2', 'gaus3', 'gaus4', 'gaus5', 'gaus6', 'gaus7', 'gaus8', 'mexh', 'morl', 'shan']
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```
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* The mexican hat wavelet "mexh"
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* The Morlet wavelet "morl"
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* The complex Morlet wavelet ("cmorB-C" with floating point values B, C)
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* The Gaussian wavelets ("gausP" where P is an integer between 1 and and 8)
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* The complex Gaussian wavelets ("cgauP" where P is an integer between 1 and 8)
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* The Shannon wavelets ("shanB-C" with floating point values B and C)
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* The frequency B-spline wavelets ("fpspM-B-C" with integer M and floating point B, C)
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see [Choosing the scales for cwt](https://pywavelets.readthedocs.io/en/latest/ref/cwt.html#choosing-the-scales-for-cwt)
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## Visualizing wavelets
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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import pywt
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wavelet_name: str = "cmor1.5-1.0"
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# "linked" to how many peaks and
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# troughs the wavelet will have
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scale: float = 10
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# Invoking the complex morlet wavelet object
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wav = pywt.ContinuousWavelet(wavelet_name)
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# Integrate psi wavelet function from -Inf to x
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# using the rectangle integration method.
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int_psi, x = pywt.integrate_wavelet(wav, precision=10)
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int_psi /= np.abs(int_psi).max()
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wav_filter: np.ndarray = int_psi[::-1]
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nt: int = len(wav_filter)
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t: np.ndarray = np.linspace(-nt // 2, nt // 2, nt)
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plt.plot(t, wav_filter.real, label="real")
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plt.plot(t, wav_filter.imag, label="imaginary")
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plt.ylim([-1, 1])
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plt.legend(loc="upper left")
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plt.xlabel("time (samples)")
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plt.title(f"filter {wavelet_name}")
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```
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