When is a continuous wavelet in the Schwartz space?

1. What does a continuous wavelet transform do?
2. What is the difference between continuous wavelet transform and discrete wavelet transform?
3. What is the wavelet transform and when should it be used?
4. What are the types of wavelet?

What does a continuous wavelet transform do?

In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously.

What is the difference between continuous wavelet transform and discrete wavelet transform?

The CWT and the discrete wavelet transforms differ in how they discretize the scale parameter. The CWT typically uses exponential scales with a base smaller than 2, for example 2^1/12 . The discrete wavelet transform always uses exponential scales with the base equal to 2.

What is the wavelet transform and when should it be used?

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 are the types of wavelet?

There are two types of wavelet transforms: the continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). Specifically, the DWT provides an efficient tool for signal coding.