Re: Two DSP theoretical questions
- From: Tim Wescott <tim@xxxxxxxxxxxxxxxx>
- Date: Fri, 15 Feb 2008 00:05:12 -0600
On Thu, 14 Feb 2008 12:28:06 -0600, scc28 wrote:
(top posting fixed)
Yes:
On Tue, 12 Feb 2008 17:06:13 -0600, scc28 wrote:
Hi, I have two questions which seem somewhat basic but confuse me:
1. We know that a sequence has to be "summable" to have Fourier
Transform (ie. DTFT converges). Is this the same as saying that a
"bounded" sequence will have Fourier Transform?
No. If x_n = 1 for all n from 0 to infinity, then the sum of all x_n is
infinite, even though x_n is pretty strongly bounded.Hi thanks for the helpful insight. I guess I need to rephrase my 2nd
2. Do all sequences have z-transform? In other words, can a sequenceRandy's answer: nuh uh. The z transform is the result of a sum, if the
have z-transform with no ROC (region of convergence)?
sum doesn't converge for any z then it's 'answer' is meaningless.
question. If a z transform of a sequence does not have any ROC, can it
still be written in a closed mathematical expression?
thanks in advance
X(z) = e^(j * theta(z)) * infinity
That's assuming you're good enough to solve an unbounded summation for
the phase angle, of course.
--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com
Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
.
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