In systems analysis, wavelet transform is used compared to Fourier transform, because wavelets are functions in which most of their energy is concentrated over a short period of time and converges rapidly.
Are there any articles that discuss the applications of wavelet transform?
Wavelet transform (WT) are very powerful compared to Fourier transform (FT) because its ability to describe any type of signals both in time and frequency domain simultaneously while for FT, it describes a signal from time domain to frequency domain. A major disadvantage of the Fourier Transform is, it captures global frequency information, meaning frequencies that persist over an entire signal. This kind of signal decomposition may not serve all applications well. Therefore, an alternative approach is needed i.e. Wavelet Transform, which decomposes a function into a set of wavelets.
The key advantage of the WT compared to FT is the ability to extract both local spectral and temporal information. Apart from this, if you know what characteristic shape you are trying to extract from your signal, there are a wide variety of wavelets to choose from to best match that shape.
The following articles are discussing the applications of wavelet transform:
1. Rhif, Manel, et al. "Wavelet transform application for/in non-stationary time-series analysis: a review." Applied Sciences 9.7 (2019): 1345.
2. Sui, Kun, and Hyung-Gi Kim. "Research on application of multimedia image processing technology based on wavelet transform." EURASIP Journal on Image and Video Processing 2019.1 (2019): 1-9.
3. Silik, Ahmed, et al. "Comparative analysis of wavelet transform for time-frequency analysis and transient localization in structural health monitoring." Structural Durability & Health Monitoring 15.1 (2021): 1.
4. Kaloop, Mosbeh R., et al. "A wavelet-Particle swarm optimization-Extreme learning machine hybrid modeling for significant wave height prediction." Ocean Engineering 213 (2020): 107777.
Wavelets are old enough that you will find many books about numerous applications. Just look for "wavelet applications" on Amazon for example or in your University library for books on the topic.
Personally, as the subject is mature, I would start with 1 or 2 good books instead of more specialized papers.
-The main difference is that wavelets are localized in both time and frequency whereas the standard Fourier transform is only localized in frequency
-Wavelet transform (WT) are very powerful compared to Fourier transform (FT) because its ability to describe any type of signals both in time and frequency domain simultaneously while for FT, it describes a signal from time domain to frequency domain.
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