calculating daubechies coefficients

I understand that you perform the inner products of the signal with
the wavelet and the scaling functions to get the coefficients. But I
have two questions about the prcoess:

  1. Do I perform the products of all three variables (ie:  
signal.scaling.wavelet) to get the coefficients, or do I perform two
separate calculations (ie: signal.scaling and signal.wavelet)?
  
  2. What values of the signal do I use in the calculation (ie: do I
use the frequency, the amplitude, the phase, etc.)?

Any help will be much appreciated.

David Saunders

DavidSaunders9 wrote:
> I understand that you perform the inner products of the signal with
> the wavelet and the scaling functions to get the coefficients. But I
> have two questions about the prcoess:
> 
>   1. Do I perform the products of all three variables (ie:  
> signal.scaling.wavelet) to get the coefficients, or do I perform two
> separate calculations (ie: signal.scaling and signal.wavelet)?

If the context of your question is a sampled data system, I 
would say here that you perform two convolutions.  The 
convolution is a running inner product.  For each new 
sample, you form the two inner products with the last n 
samples to get the next two coeficients.

>   
>   2. What values of the signal do I use in the calculation (ie: do I
> use the frequency, the amplitude, the phase, etc.)?

The last n discrete sample values where n is the length in 
samples of your wavelet and your scaling function.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Thank you for your reply, but I am still a bit confused. 

In an example calculation I read it referred to the signal as being
[3,1,-2,4]. Are these four numbers the values of the sample at t = 0,
1, 2, 3?



Bob Cain <arcane@arcanemethods.com> wrote in message news:<clbir202dcf@enews4.newsguy.com>...
> DavidSaunders9 wrote:
> > I understand that you perform the inner products of the signal with
> > the wavelet and the scaling functions to get the coefficients. But I
> > have two questions about the prcoess:
> > 
> >   1. Do I perform the products of all three variables (ie:  
> > signal.scaling.wavelet) to get the coefficients, or do I perform two
> > separate calculations (ie: signal.scaling and signal.wavelet)?
> 
> If the context of your question is a sampled data system, I 
> would say here that you perform two convolutions.  The 
> convolution is a running inner product.  For each new 
> sample, you form the two inner products with the last n 
> samples to get the next two coeficients.
> 
> >   
> >   2. What values of the signal do I use in the calculation (ie: do I
> > use the frequency, the amplitude, the phase, etc.)?
> 
> The last n discrete sample values where n is the length in 
> samples of your wavelet and your scaling function.
> 
> 
> Bob

DavidSaunders9 wrote:

> Thank you for your reply, but I am still a bit confused. 
> 
> In an example calculation I read it referred to the signal as being
> [3,1,-2,4]. Are these four numbers the values of the sample at t = 0,
> 1, 2, 3?

If that's what they called the signal, then yes.

BTW, I highly recommend "Wavelets and Filter Banks" by 
Strang and Nguyen as a pedagogic resource.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein