RE: Re: Nyquist
Posted by
Harrison, Doug
on 2000-01-18 12:06:10 UTC
The Nyquist theorem states that if you sample a periodic function at
anything more than twice that function's highest frequency component then
you can completely describe that function. Occasionally, some astute
individual (or smart-ass mathematician) will reply that it only works if all
components of the function are sinusiodal.
But, replies the engineer, according to Fourier all periodic wave forms can
be represented as a series of sine waves, so it works for all continuous
functions. And if we break a few more rules we can even apply it to
transient functions and piece-wise continuous functions.
Says the mathematician, that's the problem with you engineers - always
breaking the fundamental rules of mathematics.
Says the engineer, how much did you make last year?
Mathematician: Well, er, um . . .that's not the issue!
Thus goes the life of a frustrated scholar of mathematics. They reportedly
make good lovers though. I read somewhere that the reason there is no Nobel
prize for Mathematics is because the gentleman who should have received the
first one was at the time having an affair with the wife of a Nobel
committee member.
Anyway, you need some amount greater than two samples per cycle of the
highest frequency you wish to process.
Doug
anything more than twice that function's highest frequency component then
you can completely describe that function. Occasionally, some astute
individual (or smart-ass mathematician) will reply that it only works if all
components of the function are sinusiodal.
But, replies the engineer, according to Fourier all periodic wave forms can
be represented as a series of sine waves, so it works for all continuous
functions. And if we break a few more rules we can even apply it to
transient functions and piece-wise continuous functions.
Says the mathematician, that's the problem with you engineers - always
breaking the fundamental rules of mathematics.
Says the engineer, how much did you make last year?
Mathematician: Well, er, um . . .that's not the issue!
Thus goes the life of a frustrated scholar of mathematics. They reportedly
make good lovers though. I read somewhere that the reason there is no Nobel
prize for Mathematics is because the gentleman who should have received the
first one was at the time having an affair with the wife of a Nobel
committee member.
Anyway, you need some amount greater than two samples per cycle of the
highest frequency you wish to process.
Doug
> -----Original Message-----
> From: Ray Henry [SMTP:rehenry@...]
> Sent: Tuesday, January 18, 2000 10:52 AM
> To: CAD_CAM_EDM_DRO@onelist.com
> Subject: [CAD_CAM_EDM_DRO] Re:
>
> From: Ray Henry <rehenry@...>
>
>
> Jon
>
> -----om-----
> <big snips all over the place>
> > From: Jon Elson <jmelson@...>
> >Subject: Re: Re: Closed loop steppers
>
> >Well, yes, there is a jerk during a crash
>
> Yes, and it was me! I wired the two prox switches in a tool measuring
> stand backwards and when we measured a 3/8 drill bit the axis went
> into rapid when it touched the first prox. Other than the butt end in
> the tool holder, we never found even a sliver of the bit nor heard it hit
> anything. When I looked around, the operator was checking himself for
> major blood leaks. I was properly humbled. (some will say, "Yea but
> you got most of it back." :-)
>
> >In my own EMC / servo setup, EMC is recomputing velocity 1000 times
> >a second, but the servo amp is actually providing higher bandwidth than
> >you would get from EMC, which the Nyquist theorem would limit to
> >less than 500 Hz.
>
> Knew a Nyquist once. He was a grounds keeper. What's the theorem and
> why is 500 Hertz a theoretical limit here?
>
> Ray
>
>
>
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