Comparative Analysis of Wavelet and Hilbert Transform Algorithms Applied to the Same Signal

Wavelet Transform and Hilbert Transform are two commonly used signal processing algorithms capable of analyzing the same signal. Wavelet Transform operates as a multi-resolution analysis method that decomposes signals into different frequency components through scalable wavelet functions. In practical implementations using MATLAB or Python, engineers typically employ functions like wavedec() or pywt.wavedec() to perform multi-level decomposition, enabling extraction of characteristic features across various frequency bands. Hilbert Transform serves as a time-frequency analysis technique that decomposes signals into simultaneous time and frequency components using convolution with 1/πt. Code implementations often utilize functions like hilbert() in MATLAB or scipy.signal.hilbert() in Python, which generate analytical signals to reveal both temporal and spectral characteristics through instantaneous frequency calculations. By comparing these two algorithms, engineers can better understand fundamental signal processing principles and select appropriate methods for specific applications. Wavelet Transform excels in capturing transient features and non-stationary signal components, while Hilbert Transform provides superior time-frequency localization for monocomponent signals. Practical implementation considerations include选择合适的母小波类型 for wavelet analysis and managing boundary effects in Hilbert Transform applications.