Disadvantages of wavelet transform

Question

I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information about at which time it happens. That's why the wavelet transform is suitable for the time-frequency analysis. It is also good for signal denoising, but of course it has some disadvantages.

So I would like to know what are main advantages of the wavelet transform? Is it good for spectral estimation; like finding amplitudes, frequencies and phases, or it just helps us to find discontinuous and irregularities of a signal?

Thanks in advance

Answer 1

If you consider the whole set of potential wavelet transforms, then you have a lot of flexibility.

For instance, should you use 1D continuous complex wavelet transforms, by analyzing the modulus and the phase of the scalogram, and provided you use well-chosen wavelets (potentially different for the analysis and the synthesis), and a proper discretization, you can:

• find discontinuities and irregularities of a signal and its derivatives
• find break point location by wavelet ridge extrapolation
• denoise
• perform matched filtering based on templates (with complex continuous or discrete dual-tree wavelet frames)
• analyse (multi-)fractalty
• analyse frequencies (with Gabor wavelets for instance)

Due to the redundancy, and the quantity of available wavelets (not the same is best for different purposes), they could appear a little less efficient for the analysis of pure stationary and harmonics signals, for which Fourier is better suited.

The main drawbacks are:

• for fine analysis, it becomes computationaly intensive
• its discretization, the discrete wavelet transform (comp. efficient), is less efficient and natural
• it take some energy to invest in wavelets to become able to choose the proper ones for a specific purpose, and to implement it correcly.

Answer 2

Now depending what type of signal you have wavelets may be convenient or not, as far as know if yours signal is irregular non stationary non periodic and do not want to go crazy into making your signal stationary which sometimes can be fairly difficult the best way to go is with wavelets, now the issues with wavelets for anayzing signals in a discrete manner instead than in a continuous manner is that the aproximation functions may be off sometimes significanly than the signal they want to model. This is an issue as in denosing or threholding or even modeling as the coefficients may not represent the signal with sufficient accuracy in the time domain and also in the frequency domain.