Continuous wavelet transform subsampling at lower frequencies?

1. How does continuous wavelet transform work?
2. What is the difference between continuous wavelet transform and discrete wavelet transform?
3. What is the disadvantage of wavelet transform?
4. What is the main advantage of wavelet analysis over STFT?

How does continuous wavelet transform work?

Continuous wavelet transform (CWT) is defined as adding all the time signals and multiplying by the shift version of the wavelet. The output of the continuous wavelet transform gives the wavelet coefficients as the output. These coefficients are functions of scale and position.

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 disadvantage of wavelet transform?

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information.

What is the main advantage of wavelet analysis over STFT?

Wavelet analysis overcomes the disadvantage of STFT since CWT uses a windowing technique with variable sized regions. Wavelet analysis allows the use of long time intervals where we want more precise low-frequency information, and shorter regions where we want high-frequency information.