Wavelet-Based Spectrum Analyzer!

FFT has long been the go-to method for visualizing audio spectra, but what if there’s a faster and more efficient alternative? Enter the Haar Wavelet Transform: a technique that provides logarithmic frequency resolution while being even more computationally efficient than FFT-based analysis.

Stay tuned for a deep dive into how wavelets can be used real-time spectral analysis—no FFTs required!

Some preview: https://gist.github.com/ashafq/99d468dc5e52c7bea23ad4824e21161f

Hubbard’s “The World According to #Wavelets” is, by far, the most accessible book on the subject for non-engineers.

MotionWavelet: Human Motion Prediction via Wavelet Manifold Learning

Authors: Yuming Feng, Zhiyang Dou, Ling-Hao Chen, Yuan Liu, Tianyu Li, Jingbo Wang, Zeyu Cao, Wenping Wang, Taku Komura, Lingjie Liu

pre-print -> https://arxiv.org/abs/2411.16964
website -> https://frank-zy-dou.github.io/projects/MotionWavelet/

'ptwt - The PyTorch Wavelet Toolbox', by Moritz Wolter, Felix Blanke, Jochen Garcke, Charles Tapley Hoyt.

http://jmlr.org/papers/v25/23-0636.html

#wavelet #wavelets #pytorch

Here's a bit of technical content from me - today a deep dive on #baseline correction methods.

Baseline correction is a preprocessing technique to remove background signal and isolate peaks in hashtag#spectroscopy data.

In my recent post I discuss two methods:
1. Wavelet transform (WT) - Decomposes signal into components at different frequencies. Lowest frequency component represents baseline and can be removed.
2. Asymmetric least squares (ALS) - Fits a smooth baseline function, penalising positive deviations more than negative ones.

TL;DR: WT method is intuitive but can distort peaks. ALS produces better results.

Both methods are applied on a #Raman spectrum and an X-ray fluorescence (#XRF) spectrum. ALS gives a cleaner baseline correction and it's effective for removing broad, slowly varying background while preserving sharper spectral features.

#chemometrics #Python #MachineLearning #wavelets #regression

https://nirpyresearch.com/two-methods-baseline-correction-spectral-data/

"Binlets: Data fusion-aware denoising enables accurate and unbiased quantification of multichannel signals", Silberberg & Grecco, 2023 https://www.sciencedirect.com/science/article/pii/S1566253523003159

Old school signal processing, not based on machine learning but instead on a translation-invariant Haar wavelet decomposition, profitably exploiting correlations across channels. The manuscript includes an accessible and brief "Theory" section and a longer appendix. All it needs to run is a test function between two data points.

In their benchmarks and use cases, the new method outperforms existing denoising methods. In both time series and on fluorescent microscopy images.

There's a repository available https://github.com/maurosilber/binlets and can be installed with `pip install binlets`.

Wavelet decomposition is very popular in image analysis and processing. Here's my attempt to share some code to perform spectral smoothing (or denoising, to be fancy) using the same principle.

Wavelet denoising of spectra • NIRPY Research
https://nirpyresearch.com/wavelet-denoising-spectra/

Can the Continuous Wavelet Transform (CWT) improve the predictions of your deep / machine learning models?

Reduced chance of over-fitting to noise, or other anomalies, in your raw data. Resulting in simpler lightweight models.

A powerful preprocessing technique.

https://medium.com/mlearning-ai/the-power-of-the-continuous-wavelet-transform-cwt-in-machine-learning-980e80ecfb8a

i know what #wavelets are, now .

https://www.youtube.com/watch?v=jnxqHcObNK4

Can someone help?
https://dsp.stackexchange.com/questions/79418/calculate-and-plot-cdf-5-3-wavelet-phi-and-psi-functions
#wavelets #cdf #dsp