ECG Signal Processing: Wavelet Transform Modulus Maxima Detection and Multiresolution Analysis

This implementation provides detailed functionality through three specialized functions. The primary function handles ECG signal reading and wavelet transform modulus maxima sequence detection, which is crucial for identifying potential cardiac abnormalities through peak characteristic analysis. The modulus maxima detection typically involves calculating wavelet coefficients' local extrema to pinpoint significant signal features. The second function serves as a subroutine for multiresolution decomposition using the à trous algorithm implementation. This algorithm employs a non-decimated wavelet transform approach that maintains constant data length across all decomposition levels. During processing, it generates both detail coefficients (capturing high-frequency components) and approximation coefficients (representing low-frequency trends) at each resolution level, all preserving the original signal's length through symmetric padding or circular convolution techniques. The third function operates as a reconstruction subroutine within the multiresolution analysis framework. It performs inverse wavelet transformation to reconstruct the original signal from the multilevel decomposition coefficients, enabling verification of decomposition accuracy and facilitating further signal processing. The reconstruction process typically involves iterative filtering operations that reverse the decomposition steps while maintaining perfect reconstruction conditions. Through integrated application of these three functions, the system achieves comprehensive ECG signal analysis with enhanced accuracy for medical diagnosis, particularly in detecting subtle morphological changes indicative of various cardiac conditions.