[music-dsp] useful math?

[Bob Grove]

Oh GOD!  I'll have to review my texts, I don't have a PhD and this is a long
time ago, so perhaps I'm still confused...
but here's an example that comes to mind.  So, please be gentle if I'm
talking about of my a@@ right now but here is one that I remember
(and maybe I'm wrong)

BIBO, Oppenheim, Willsky, Signals and Systems, p. 98, ok to me they are
using absolute value signs on eq 3.55, so it looks to me like absolute value
(which means that ...x[i] +- x[i+1]... and so forth are just summed inside
the absolute value sign..
i.e. I don't think |x[n]| < B for all n is technically correct I think it
should be ||x[n]|| < B or integral(|x[n]|) but not just |x[n}|..

the rest seems aok, because it's a summation, => absolutely integratable,
but the input doesn't to me.

to me at least it's confusing, so I guess you can take that as a dusty
student who remembers this stuff...say one is deciding if the sequence
x[n] = (-1)^n, -inf < n < inf is Bounded...

well, if I'm thinking I can just take the abs versus the modulus or L1 norm
of the input I just flunked the test (and my signal blew up the lab),
whereas if I see the l1 norm there, I know it's not convergent (not less
than B for all n).

(I hope I just didn't embarrass myself on this list, but hell, you asked
that's one that bugged me in school)

(I guess this one does reference Churchill per say, but it is one that I
remember, there are many of these things that really bothered me
and I went for the math books to clarify, but the Churchill does define
complex modulus so you either got it together or flunked :))

(yes I kept all of my school books)
 

-----Original Message-----
From: robert bristow-johnson [mailto:rbj at audioimagination.com] 
Sent: Monday, November 28, 2005 8:36 PM
To: music-dsp
Subject: Re: [music-dsp] useful math?

on 11/28/2005 20:48, Bob Grove at music-dsp at musemagic.com wrote:

> Complex analysis, has proofs but really useful and very helpful in 
> doing DSP...esp for complex analysis has the correct notation and more 
> than once I have found incorrect notation in various DSP books...which 
> makes it confusing as to what's going on (at least to me).

other than the "i" vs. "j" notation, the only confusing notation or
terminology issue i have ever seen between the two is "analytic function".
Bob, what other notation problem have you seen (in DSP texts where it is
corrected in complex variables texts)?

-- 

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."


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