Discrete wavelet transform - DWT (beginner)

1. How does DWT work?
2. How do you calculate discrete wavelet transform?
3. Why do we use DWT?
4. What are basics of wavelet transforms?

How does DWT work?

A discrete wavelet transform (DWT) is a transform that decomposes a given signal into a number of sets, where each set is a time series of coefficients describing the time evolution of the signal in the corresponding frequency band.

How do you calculate discrete wavelet transform?

cJ1(k)=〈f,φJ1,k〉=2-J1/2f(2-J1(m0+k))≈2-J1/2f(2-J1k). Thus, in practice, the finest scale J1 is determined by the sampling rate. By rescaling the function and amplifying it appropriately, one can assume the samples of f(t) are equal to the scaling function coefficients.

Why do we use DWT?

The discrete wavelet transform has a huge number of applications in science, engineering, mathematics and computer science. Most notably, it is used for signal coding, to represent a discrete signal in a more redundant form, often as a preconditioning for data compression.

What are basics of wavelet transforms?

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.