Getting Started with Continuous Wavelet Transform

In the following content, we introduce an introductory program for continuous wavelet transform. This program provides an algorithmic implementation of the Morlet wavelet transform, which can be applied in various fields including time series analysis, image processing, and signal processing. The implementation typically involves defining the Morlet wavelet function as a complex exponential modulated by a Gaussian window, followed by convolution operations with input signals at different scales. Continuous wavelet transform is particularly effective for decomposing non-stationary signals, offering advantages over Fourier transform in certain scenarios by capturing both time and frequency information simultaneously. This method enables better understanding of local signal characteristics and spectral features, thereby facilitating more effective data analysis and processing. The algorithm implementation includes scale parameter adjustment, wavelet coefficient computation, and time-frequency representation visualization components.