Re: Interpolation

On Tue, 01 Apr 2008 14:41:06 -0600, jim <"sjedgingN0sp"@m@mwt.net>
wrote:

>Eric Jacobsen wrote:


>> The more fundamental issue as I understand it, is whether or not a
>> filter would change the original, uninterpolated input samples in the
>> output, i.e., are the interpolated samples distinguishable from the
>> uninterpolated.   In a "decimating" filter the issue that an
>> anti-aliasing filter would necessarily change them was cited as an
>> example that even the orginal remaining (uninterpolated) samples would
>> necessarily change.   I don't think they "necessarily" will.
>
>If the process requires an AA filter to reduce bandwidth they
>"necessarily" will.

Back to my previous example with a solitary tone in a unity gain
passband.   If the decimation rate is integer and the samples are not
shifted in time, what will be different about the output samples as
compared to the corresponding input samples?
 
>> I don't think anyone has argued that output samples will remain the
>> same if the energy content of the output signal isn't the same as the
>> input.  That'd be pretty tough to argue.  It also doesn't have much to
>> do with the interpolation question, whereas I think my point did.

>	The statement was made that if you use an AA filter to reduce bandwidth 
>it changes the original sample points. Reducing bandwidth is typically
>what is required when down sampling. 
>	
>	That statement relates  to interpolation because to a purist the original
>sample points need to remain the same for it to be called interpolation.
>If that is going to be  the definition of interpolation then down sampling
>can not be interpolation (except the rare cases when you don't have to
>reduce bandwidth) And of course, when the sample rate conversion isn't
>downward then there will be no need to reduce the bandwidth and therefore
>it can be called interpolation because the original sample points can
>remain the same. 

It sounds like we have the same understanding of the problem.  

>> And since the topic is also terminology "anti aliasing" filters are
>> usually analog. 
>
> If your point is digital AA filters do not exist - then why not just say
>that? 

I wasn't making a point, I was asking a question, which you snipped:

" A decimating filter may need to be frequency
selective in order to prevent aliasing in the output, but is that
really an anti-aliasing filter or just a properly designed decimating
(or downsampling) filter?"

Since a fair portion of the discussion is about terminology, and a few
folks have been using "anti-aliasing" together with decimating
filters, I thought it was a pertinent question.  Since "anti-aliasing"
is usually an analog filter function preceding an ADC in my
experience, I'm curious how many people also apply the term to
decimating filters?   It seems unusual to me.

>>  A decimating filter may need to be frequency
>> selective in order to prevent aliasing in the output, but is that
>> really an anti-aliasing filter or just a properly designed decimating
>> (or downsampling) filter?
>
>I would think "prevent aliasing" = "anti-aliasing". 

Yes, in a general sense of just interpreting the words, but usually
when one says "anti-aliasing filter" generically the first thought is
of an analog filter preceding an ADC.  In my experience that's not
applied nearly as generically to decimating filters.   I'm curious
about other's experience there, mostly to know whether or not it does
cause confusion.   I'd hope you'd agree that reducing confusion is a
good thing, because it's really the motivation behind the terminology
discussion.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org