Wavelet transform in r

1. What is wavelet transform used for?
2. What is meant by wavelet transform?
3. What is the difference between wavelet and Fourier transform?
4. Is wavelet transform a convolution?

What is wavelet transform used for?

The wavelet transform (WT) can be used to analyze signals in time–frequency space and reduce noise, while retaining the important components in the original signals. In the past 20 years, WT has become a very effective tool in signal processing.

What is meant by wavelet transform?

Wavelet transforms are mathematical tools for analyzing data where features vary over different scales. For signals, features can be frequencies varying over time, transients, or slowly varying trends. For images, features include edges and textures.

What is the difference between wavelet and Fourier transform?

While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal.

Is wavelet transform a convolution?

A wavelet transform is essentially a convolution with a bunch of functions chosen to be “compact” in frequency and time. Here compact means that the functions are nonzero only over a limited range of frequency and time.