InvertibleWavelets

A lightweight, fully invertible wavelet transform toolkit for Python — implement time-frequency filterbanks, run forward/inverse transforms, and visualize scalograms with ease.

Features

• Abstract FilterBank base class with pluggable implementations:
  • LinearFilterBank (linear-scale center frequencies)
  • DyadicFilterBank (dyadic/power-of-two scales)
• FFT-based forward and inverse transforms with overlap-add handling
• frame operator normalization built in to assist the dual-frame inverse
• Scalogram plotting (log-power over time–frequency)
• Four canonical mother wavelets:
  • Morlet, Cauchy, MexicanHat, DoG
• Pure Python, minimal dependencies (numpy, scipy, matplotlib)

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Installation

Install directly from GitHub (no PyPI publish required):

pip install git+https://github.com/aphoffmann/invertiblewavelets.git

Quickstart

import numpy as np
import matplotlib.pyplot as plt

from invertiblewavelets import LinearFilterBank, DyadicFilterBank, Transform, Morlet

# 1. Create a test signal
fs = 1000                       # sampling rate [Hz]
N = 10_000
t = np.arange(N)/fs
data = np.sin(2*np.pi*100*t)

# 2. Create a Filterbank
fb  = LinearFilterBank(
    wavelet=Morlet(fc=1, fb=100),
    fs=fs, 
    N=N, 
    b = 1/10, 
    real=False
)

fb_dyadic = DyadicFilterBank(
    wavelet=Morlet(fc=1, fb=100),
    fs=fs,
    N = N,
    s_max = 1/10,
    real=False
)

# 3. Build the Transform with the filterbank
xfm = Transform(fb.Wfreq)

# 4. Forward
xfm.forward(data, mode='full')

# 5. Plot scalogram
xfm.scalogram(coeffs, title="Demo Scalogram")
plt.show()

# 6. Inverse
reconstructed = xfm.inverse(coeffs, mode='full', Lx = N)

# 7. Print RMSE
print(np.sqrt(np.mean((data-reconstructed)**2)))