It depends on what you want to get after the decomposition.

Adding to the answer from Aleksey Kudreyko: Each decomposition level indicates a band of frequency. So if you increase the no. of decomposition level then each band will be narrower which means you will have better frequency resolution. You can easily know what exactly the frequency range of a particular level if you know the sampling frequency of your original audio signal. The attached link may be useful in understanding the frequency band of different levels. 

http://www.mdpi.com/entropy/entropy-16-06553/article_deploy/html/images/entropy-16-06553f5-1024.png

There is no deterministic method for the decomposition

You should test all decompositions to see the deference's

Hi Johanes,

The maximum number of levels Jmax with which a signal can be decomposed, can be determined using the following equation :

Jmax= fix(log2[(N/Nw)-1])

N is the length of the signal, Nw gives the length of the decomposition filter associated with the chosen mother wavelet and fix is to round the value in the brackets to its nearest integer. 

For example, sampling frequency of a given signal is 1024 samples/sec, you will get 5 levels, the frequency band corresponding to this sampling frequency is from -512 to 512. Let's as usual neglect the negative part for real signals. The first level trend contains 0..256, the detail 512..256. The second level trend then contains the frequencies 0..128, the second level details 256..128. Etc.

Good luck

The general rule about decomposition is depends on sampling frequency. The sampling frequency depends on Nyquist rule (as min sampling freq Fs). The original signal is having band width of Fs/2. by first level decomposition it will be divide in (0 to Fs/4) &(Fs/4 to Fs/2) the in second level it again in (0 to Fs/8) & (Fs/8 to Fs/4) and detail (Fs/4 to Fs/2) and so on. The level of decomposition is decided on the basis of desired frequency band features.

As for wavelets and their choices

I advise you to use several types of wavelet mothers with adaptive thresholding

Hello Johanes,

Wavelet is all about getting frequency information of a signal. There are several aspects to obtain a certain level of decomposition. Following are few of them.

1. Nyquist sampling rule which says that for sampling frequency Fs, first level decomposition will have frequency subbands of Fs/2. so you have to look for better frequency resolution in approximation (lower frequency) and detail (higher frequency) coefficients.

2. You can use different mother wavelet families and monitor the differences in frequency resolution.

3. One of the mostly used, is ENTROPY CRITERIA that enables you to obtain optimum level of decomposition. For more details go through below link and read "choosing the optimal decomposition".

https://in.mathworks.com/help/wavelet/ug/wavelet-packets.html

Good Luck

Vivek

Dear All,

First sory for late reply, Thank you for your interest about this question!

Maybe this can help you:

-The first step, we need to find the frequency

characteristic of the audio signal to determine the most appropriate decomposition level.

-Second, performing FFT

Last, find the frequency range corresponding to the table with wavelet decomposition levels

More detail, kindly check my journal

https://www.worldscientific.com/doi/10.1142/S0218213018500161

Good luck!

Johanes Andre

Try to use the

pywt.wavedec(eeg_data, wavelet = 'db4', level=3)

The wavedec() function performs 1D multilevel Discrete Wavelet Transform decomposition of a given signal and returns an ordered list of coefficients arrays in the form:

[cA_n, cD_n, cD_n-1, ..., cD2, cD1]

where n denotes the level of decomposition. The first element (cA_n) of the result is the approximation coefficients array and the following elements (cD_n - cD_1) are detailed coefficients arrays.

Now coming to the point of different frequency bands

Discrete wavelet transform will always return only 1 approximation coefficient.

If starting frequency band of the neuroelectric waveform is 0-64 Hz then at level =1 we will get 0-32 Hz which gives approximation coefficients & another band is 32-64Hz which gives the detail coefficient of the wavelet.

At level = 2, the discrete wavelet transform will return 3 frequency bands:

1. 0-16 Hz i.e. approximation coefficients

2. 16-32 Hz i.e. detail coefficients

3. 32-64 Hz i.e. detail coefficients.

At level= 3, we will have 4 frequency bands:

1. 0-8Hz, i.e. approximation coefficients

2. 8-16Hz, i.e. detail coefficients

3. 16-32Hz, i.e. detail coefficients

4. 32-64Hz, i.e. detail coefficients

Hope this will help you.

https://pdfs.semanticscholar.org/91b1/38822035f59fcdce3277582fe10386ca00af.pdf

ttps://pdfs.semanticscholar.org/91b1/38822035f59fcdce3277582fe10386ca00af.pdf