Multiwavelet Decomposition of 1D Signals with Implementation Details

Before performing multiwavelet decomposition on 1D signals, the signal must undergo pre-filtering processing. Pre-filtering involves applying a low-pass filter to the signal during the decomposition process to remove high-frequency noise. In code implementation, this typically involves designing or selecting an appropriate low-pass filter (such as FIR or IIR filters) and applying convolution operations to the input signal. The filtered signal then serves as input for the subsequent wavelet decomposition stage. Following pre-filtering, specific wavelet coefficients are loaded from the coefficient file (coef). These coefficients are utilized during the decomposition process. Wavelet coefficients represent the signal's variations at different scales and positions obtained through wavelet decomposition. In programming terms, the coefficient file usually contains filter bank coefficients (both low-pass and high-pass filters) that define the multiwavelet transform. The decomposition algorithm typically involves iterative filtering and downsampling operations using these coefficients through convolution and decimation steps. Therefore, correctly loading and applying wavelet coefficients is a crucial step in wavelet decomposition. The implementation requires careful handling of coefficient file formats (such as text files or binary files) and proper parameter initialization for the decomposition algorithm to ensure accurate multi-resolution analysis of the input signal.