Time Support and vanishing moments

Started by October 13, 2005
```Hi everybody,

I was going through the wavelets basics. How is Time support and
vanishing moments relate to each other? I am trying to get hang of it
but there is too much mathematics involved and sometimes I feel lost ?

Can someone help me understand the underlying concept?

I will be grateful.

Thanks

Vijay Pal

```
```"VPSA" <vpsanand@gmail.com> wrote in message
> Hi everybody,
>
> I was going through the wavelets basics. How is Time support and
> vanishing moments relate to each other? I am trying to get hang of it
> but there is too much mathematics involved and sometimes I feel lost ?
>
> Can someone help me understand the underlying concept?
>

I would Google, look for pictures, etc.

I'm not a wavelet expert by any means - but:

If a waveform is the impulse response of a perfect lowpass filter (purely
zero response in the stopband >=fc) ...
and
If this lowpass filter has multiple zeros at fc then the impulse response
decays faster in relation to the number of these zeros.  I think that must
affect the higher order moments.

Now, if you flip the Fourier Transform around then this says that a
time-limited waveform (which by definition is zero at the edges) will have a
frequency spectrum that decays as 1/f^x where x is related to the number of
zeros at the edge of the time function.
The time function is of limited support and, I believe, the spectral
character of that same function will have moments related to the length of
the time function and the number of zeros at the edge (i.e. how smoothly it
reaches the zero edges).

I hope this helps a bit...

Fred

```
```Thanks Fred.

I think I have got what you are saying.

Cheers !!

```