Continuous Wavelet Transform Implementation Based on Morlet Wavelet

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Resource Overview

Custom implementation of continuous wavelet transform using Morlet wavelet with adjustable parameters. The function accepts three input variables: signal data, signal length, and decomposition levels. Returns three output variables: wavelet coefficients, frequency information, and scale parameters. This implementation performs nLevel wavelet decomposition on input signals. Users can directly call this function after providing required inputs. Note: Output differs from MATLAB's built-in cwt function - users should verify algorithm compatibility with their specific input/output requirements. The current implementation is functional but undergoing refinement.

Detailed Documentation

This article presents a continuous wavelet transform implementation based on the Morlet wavelet function. The algorithm allows parameter customization to adapt to different datasets. The core functionality requires three input parameters: the input signal, signal length, and decomposition levels (nLevel). The implementation returns three output components: wavelet coefficients, frequency data, and scale parameters corresponding to the wavelet decomposition.

The code structure implements multi-level wavelet decomposition through a scalable framework where users can modify Morlet wavelet parameters like center frequency and bandwidth. Key algorithmic steps include signal preprocessing, wavelet kernel generation, and convolution-based coefficient calculation across multiple scales.

Important note: This custom implementation produces different results compared to MATLAB's built-in cwt function due to variations in normalization and boundary handling. Users should perform validation checks to ensure output meets their specific requirements. The current codebase is operational but undergoing optimization for improved accuracy.

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