I have attached the figure to understand the frequency arrangement of the wavelet packet. How from {depth=8, index=0}= the approximation boundary is 86?
I would like to know if the sampling frequency is Fs=16000 and an audio signal is decomposed to different bands; How can I define the frequency boundary for each band ?
Your qestion is insufficient. If you do not know what your application I you do not have any idea what you would like to know. Wavelet packet filter are designed based on the application. Here: what wavelets are used? What is the sampling freqeuncy? Etc., etc, etc.
Please explain what you would like to know in detail and in a more scientific (rigor) way.
As Volker well said above, your question is incomplete and it is unlikely that anyone can tell you what you want to know with such incomplete question.
Let's ask it by MATLAB code. I think it will help to say my question properly:
level=4;
wpt = wpdec(wave,level,'sym8');
cfs= wpcoef(wpt,[4 2]);
Now what is the frequency range of cfs ?
Thanks.
Dear Amir,
sorry, you didn't get it or I misunderstood you question. Even by using Matlab's m-code you will NOT get the answer regarding your question. You are asking for a frequency range, of course, in [Hz]. But without a definition of the sampling frequency this is not possible! I recommend to read a beginners book in signal processing first. This is my honest recommendation I have for you.
Dear Amir,
Wavelet gave pseudo frequencies, not exact sinusoidal frequencies. Try to find out the corresponding center frequencies in matlab for Sym 8 using ur sampling frequencies. Matlab has the code to find out the pseudo frequencies. I am providing the link below -
http://www.mathworks.com/help/wavelet/ref/scal2frq.html
Read this paper -
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1261751&tag=1
However, most of the studies don't consider pseudo frequencies. They decompose the signal content by taking Nyquest frequency level as the maximum. Suppose if your sampling frequency is 1000 Hz. The corresponding frequencies at level 4 would be - (Level 1 : 250-500 Hz, Level 2 : 125-250Hz, Level 3: 62.5-125 Hz, and Level 4: 31-62 Hz..). I myself checked the frequency levels of this method. It exactly follow the power frequency band of discrete Fourier transform.
Read the below paper too.
http://www.jelectromyographykinesiology.com/article/S1050-6411%2813%2900112-0/abstract
Dear Amir,
Based of your frequency band of interest You should find the level of decomposition related with sampling frequency , every level have half of the previous level samples.
Fs=2^n
Fs=Sampling frequency and n=wavelet level.
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