Wavelet Decomposition and Reconstruction Functions

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The process includes the following key steps:

(1) Wavelet Decomposition of Signals: Perform wavelet decomposition on signals to extract their frequency components. This typically involves using functions like wavedec() in MATLAB, which decomposes the signal into approximation coefficients (low-frequency components) and detail coefficients (high-frequency components) across multiple resolution levels.

(2) Threshold Quantization of High-Frequency Coefficients: Apply threshold quantization to the high-frequency coefficients obtained from wavelet decomposition to minimize noise impact. This step commonly uses thresholding functions such as wthresh() with soft or hard thresholding algorithms, where coefficients below a certain threshold are set to zero or reduced in magnitude to suppress noise while preserving important signal features.

(3) Wavelet Reconstruction of Signals: Reconstruct the signal using both the decomposed wavelet coefficients and the quantized high-frequency coefficients to restore the original signal's characteristics. The reconstruction process employs functions like waverec() which combines the modified coefficients through inverse wavelet transform, effectively rebuilding the denoised signal while maintaining its essential structure.

These steps represent the core workflow for wavelet-based signal analysis and reconstruction, providing an effective method for signal processing and noise reduction applications.