An Algorithm for the Continuous Morlet Wavelet Transform

TL;DR

This paper presents an efficient algorithm for computing the continuous Morlet wavelet transform, compares its energy density results with Fourier power spectra, and demonstrates its practical applications.

Contribution

It introduces a new efficient algorithm for the continuous Morlet wavelet transform and provides a framework for evaluating and applying it effectively.

Findings

The algorithm computes the transform efficiently.

Wavelet energy density aligns with Fourier power spectra.

Examples demonstrate practical utility.

Abstract

This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given. The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.