Applications of Wavelets in Signal Processing

In the field of signal processing, wavelets find extensive applications. By utilizing wavelet transforms for signal decomposition and reconstruction, signals can be better understood and processed. Wavelet decomposition typically involves breaking down signals into different frequency components using filter banks, with common implementations like the Discrete Wavelet Transform (DWT) employing pyramid algorithms through functions such as wavedec() in MATLAB. Reconstruction reverses this process using functions like waverec() to reassemble the signal from wavelet coefficients.

Additionally, wavelets enable noise reduction through thresholding techniques, significantly improving signal quality and accuracy. This involves applying soft or hard thresholding to wavelet coefficients using algorithms like Donoho's thresholding method, implemented via wthresh() and wdenoise() functions. The key advantage of wavelet analysis lies in its multiscale analysis capability, which effectively captures signal details and variations across different resolutions. Consequently, wavelets play a vital role in signal processing and are widely adopted in practical applications including biomedical signal analysis, image compression, and feature extraction.