wavelet decomposition of a signal

hi, i want to decompose a signal with wavelet in 5 subbands:

delta (0–4 Hz), theta (4–8 Hz), alpha (8–15 Hz), beta (15–30 Hz), and gamma (30–60 Hz) ,use db4"_

i found wavelet toolbox menu but cant use it,can you help me?

thanks.

Answer 1

[Jan]

Use wavedec() to calculate the wavelet decomposition and wenergy to extract the energie in the decomposition.

e.g.:

 [C, L] = wavedec(signal, waveorder, wavekind);
 [~, energies] = wenergy(C, L);

Note, that the wavelet deomposition in a specific decomposition level does not exactly represent an actual frequency band. This can be only done, using trigonometric functions for decomposition - however, in hat case you end up with the discrete Fourier transform.

However, you can calculate corresponding frequencies (i.e. pseudo frequencies) for a specific wavelet family and level of decomposition (look at centfrq() on that matter). If you carefully choose the wavelet family and wavelet order, you get a wavelet decomposition, that roughly corresponds to the desired bands.

For your use case, one would choose Daubechies order 3 Wavelets and six levels of decomposition. Then the decomposition levels 1 to 5 in reverse order should just about match the required bands:

L1: gamma, L2: beta, L3: alpha, L4: theta and L5: delta.

[Afiqah Abu Samah]

Hi, I want to ask how to calculate the energy of 2-D wavelet decomposition. I know that function wenergy2 can be use, but I want to know how it can be calculated since I want to use single level 'dwt2' function and decompose the images level-by-level instead of using this; [C,S] = wavedec2(X,2,'bior3.7'). (I have my own reason why I need to decompose it like that)

If 'dwt2' is used, I can't calculate the energy using 'wenergy2' since I didn't know how to get the 'C' array.

Please help me, give me some ideas how to solve this.

Answer 2

[m]

thanks jan for attention, i run your MATLAB command but i have a signal with 120hz and 23.6s and want to use db4 in 4 level , in your answer i cant understand who can i do it ?

(excuse me for my poor english!)

[Jan]

You will have to look into the theory of Wavelet decomposition to be able to apply it correctly. If you send me a private message, I can provide you some literature...

[m]

ok,thanks.

[Jan]

I just sent you a mail to [e-mail]