Waveletbases
Wavelet bases are a fundamental concept in signal processing and mathematics, offering a powerful alternative to traditional Fourier analysis. Instead of decomposing a signal into simple sine and cosine waves of infinite extent, wavelet bases use localized wave-like functions called wavelets. These wavelets are typically short, oscillating waveforms that decay rapidly. The key advantage of wavelet bases lies in their ability to capture both the frequency content and the temporal location of features within a signal.
A wavelet basis is formed by a set of functions derived from a single "mother wavelet" through
The construction of wavelet bases can be achieved through various methods, including orthogonal, biorthogonal, and non-orthogonal