Implementing Continuous Wavelet Transform on Signals

When performing Continuous Wavelet Transform (CWT) on signals, it is recommended to avoid directly using MATLAB's built-in cwt function. Instead, alternative wavelet transform algorithms can be implemented to achieve more accurate and stable results. The selection of wavelet transform algorithms should consider signal characteristics and required precision levels. From an implementation perspective, you can create a custom CWT function by: - Implementing the convolution operation between the signal and scaled wavelet functions - Using a loop structure to iterate through different scale values - Applying proper normalization factors for each scale Additionally, signal preprocessing should be performed to reduce the impact of noise and other interference factors on the results. Before applying wavelet transform, you can implement preprocessing techniques such as: - Digital filtering algorithms (e.g., Butterworth or Chebyshev filters) for noise reduction - Downsampling methods to handle large datasets efficiently - Signal normalization to ensure consistent amplitude ranges These preprocessing steps significantly improve the accuracy and reliability of the transformation results. The implementation should include proper boundary handling and frequency response considerations for different wavelet families (e.g., Morlet, Mexican Hat, or Daubechies wavelets).