Wavelet-based spectral analysis

•Review of outstanding articles on wavelet-based spectral analysis in period 2002–13.•Wavelet transforms for noise removal and resolution enhancement.•Wavelet transforms for data compression and chemometrics modeling.•Wavelet transforms outperform other traditional signal-processing methods.

Wavelets are a topic of pure mathematics. But over the past decade, they have shown great promise and are now being adapted for a vast number of signal-processing applications. One of the main advantages of wavelet analysis is the amount of information that can be extracted from a signal. It has demonstrated unprecedented success in terms of asymptotic optimality, spatial adaptivity and computational efficiency. Applications of wavelet transform and wavelet-packet transform in spectral analysis from 2002 to 2013 are reviewed in this article, clearly stating that wavelet methods significantly outperform other traditional methods of signal processing.