Question on pole-zero cancellation

Oli Filth wrote:>>
>>         +------+
>> ---+--->| z^-L |-------------------+
>>    |    +------+                   |
>>    |                               |
>>    |              +------------+   |
>>    +------------->|+          -|<--+
>>                   | accumulate |----->
>>                   +------------+
>>
> 
> Ah! Much clearer. :)
> 
> Then yes, this *is* of course an equivalent system.
> 
> To go back to your point on complexity, the accumulator-based system is 
> an in-place implementation the unit-length delay line, so requires maybe 
> one less register move, and so you're right, it's marginally less 
> complex.  Behaviourally however, they're identical.

Yes. I hate it when I don't communicate clearly. Thanks for your patience.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Randy Yates wrote:
> Andor wrote:
> >[...]
>
> Hi Andor,
>
> I just came up with a problem with this analysis. Consider the unit
> step function, u(t). It has a "point-mass" component in the frequency
> domain at DC:
>
>   U(w) = 1/(j*w) + pi*delta(w).
>
> However, it will pass through such a cascaded system (even a
> theoretical one) without a problem, will it not?

Hi Randy,

I nearly missed this post with all the clatter going on here. Yes, you
are right (good thinking!). The same problem occurs with sinusoids
multiplied by the step function. It does not seem so easy to multiply
point masses by zero after all :-). Perhaps one has to take the
"sidedness" of the time-domain signal into account. It definitely
requires more tought!

Regards,
Andor
> 
> --Randy

Andor wrote:
> Randy Yates wrote:
> > Andor wrote:
> > >[...]
> >
> > Hi Andor,
> >
> > I just came up with a problem with this analysis. Consider the unit
> > step function, u(t). It has a "point-mass" component in the frequency
> > domain at DC:
> >
> >   U(w) = 1/(j*w) + pi*delta(w).
> >
> > However, it will pass through such a cascaded system (even a
> > theoretical one) without a problem, will it not?
>
> Hi Randy,
>
> I nearly missed this post with all the clatter going on here. Yes, you
> are right (good thinking!). The same problem occurs with sinusoids
> multiplied by the step function. It does not seem so easy to multiply
> point masses by zero after all :-). Perhaps one has to take the
> "sidedness" of the time-domain signal into account. It definitely
> requires more tought!

For you, it's "more thought" - for me, it's "two more
graduate level mathematics courses."

What recent, graduate-level math have you taken, Andor? It
seems like this is in the "real analysis" and/or "functional
analysis" area - it might be instructive to know more about
where to think about learning more.

--Randy