what are difference wavelet inverse transformation and wavelet transformation

Question

WPD = Wavelet Packet Decomposition

Hi, dear Stack Overflow. I have questions for my time-series data.

My data is a vibration of bearing in a machine or machine tool.

We know that WPD works as a filter and is divided into 4 frequency band if we apply level.2 WPD

ex) - sampling rate = 4000Hz
1. 0 ~ 500Hz
2. 500 ~ 1000Hz
3. 1000 ~ 1500Hz
4. 1500 ~ 2000Hz
by nyquist theorem

many research use wavelet transformation result

but I think that if we apply wavelet transform to signal, that result is scale domain(time domain --> scale domain, because of wavelet transformation)

that is not the exact results that we want.

we should analyze the signal in time-domain not scale domain

so after WPD, inverse wavelet transformation should apply to divided wavelet transformation results

is that right?

summary: I have 2 questions that are:

1. Is the attempt to analyze WPD results in the time domain incorrect by inverse transformation?

2. if incorrect analysis, what is wrong with it?

Answer 1

but I think that if we apply wavelet transform to signal, that result is scale domain(time domain --> scale domain, because of wavelet transformation)

• That's not true. We'd still have access to time-domain data as well as frequency-domain data.

• Basically when we pass time-series data through wavelets, we would get resolutions on both time and frequency data and that's the entire point behind wavelets and other similar time-frequency methods such as Gabor. Therefore you don't have to use inverse wavelets.