Thread Subject: The range of Frequency for Wavelet Packet & Wavelet

Dear sir:

Wavelet Packet and Wavelet are two methods of data analysis in Time-Frequency domain, and I have a few question about frequency distribution.

I have an acoustic emitter sensor , and its frequency response is 0~400kHz. If the sampling rate is 2M Hz, what is the highest frequency in Wavelet Packet and Wavelet(400k Hz or 2Mhz)?

Thank you very much!


 

"Jeff " <kun.j.chien@gmail.com> wrote in message <j7jj35$448$1@newscl01ah.mathworks.com>...
> Dear sir:
>
> Wavelet Packet and Wavelet are two methods of data analysis in Time-Frequency domain, and I have a few question about frequency distribution.
>
> I have an acoustic emitter sensor , and its frequency response is 0~400kHz. If the sampling rate is 2M Hz, what is the highest frequency in Wavelet Packet and Wavelet(400k Hz or 2Mhz)?
>
> Thank you very much!
>
>
>

Hi Jeff, both the wavelet and wavelet decompositions cover the entire frequency range from 0 to the Nyquist, which in your case is 1 MHz (half the sampling rate). The difference between the wavelet and wavelet packet transforms is the way the divide the frequency axis.

Wayne

> Hi Jeff, both the wavelet and wavelet decompositions cover the entire frequency range from 0 to the Nyquist, which in your case is 1 MHz (half the sampling rate). The difference between the wavelet and wavelet packet transforms is the way the divide the frequency axis.
>
> Wayne


Hi Wayne, Thank you for your nice response.

You said that the entire frequency range is from 0 to 1MHz in my case, so does the distribution of frequency range for Wavelet Packet and Wavelet seem like below:


Wavelet:
                                             raw data(0~1MHz)
                                               / \
       level 1 a1(0~500kHz) d1(500k~1MHz)
                                     / \
       level 2 a2(0~250kHz) d2(250k~500kHz)
                                / \
       level 3 ... ...


Wavelet Packet:

                                              raw data(0~1MHz)
                                               / \
       level 1 (1,0)(0~500kHz) (1,1)(500k~1MHz)
                                   / \ / \
       level 2 (2,0) (2,1) (2,2) (2,3)
                        (0~250kHz) (250k~500kHz) (500k~750kHz) (750k~1MHz)
                            / \ / \ / \ / \
       level 3 ... ... ... ... ... ... ... ...


Is it right? Thank you very much!

"Jeff " <kun.j.chien@gmail.com> wrote in message <j7lti8$5os$1@newscl01ah.mathworks.com>...
> > Hi Jeff, both the wavelet and wavelet decompositions cover the entire frequency range from 0 to the Nyquist, which in your case is 1 MHz (half the sampling rate). The difference between the wavelet and wavelet packet transforms is the way the divide the frequency axis.
> >
> > Wayne
>
>
> Hi Wayne, Thank you for your nice response.
>
> You said that the entire frequency range is from 0 to 1MHz in my case, so does the distribution of frequency range for Wavelet Packet and Wavelet seem like below:
>
>
> Wavelet:
> raw data(0~1MHz)
> / \
> level 1 a1(0~500kHz) d1(500k~1MHz)
> / \
> level 2 a2(0~250kHz) d2(250k~500kHz)
> / \
> level 3 ... ...
>
>
> Wavelet Packet:
>
> raw data(0~1MHz)
> / \
> level 1 (1,0)(0~500kHz) (1,1)(500k~1MHz)
> / \ / \
> level 2 (2,0) (2,1) (2,2) (2,3)
> (0~250kHz) (250k~500kHz) (500k~750kHz) (750k~1MHz)
> / \ / \ / \ / \
> level 3 ... ... ... ... ... ... ... ...
>
>
> Is it right? Thank you very much!

That is correct Jeff, but you want to be careful with wavelet packets because there is a difference between the Paley (natural) ordering and the sequency (frequency) ordering.
See the help for otnodes

>>doc otnodes

and for wpspectrum

Wayne