RE: [SI-LIST] : Nyquist Sampling Rate

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From: AA (alokbya@yahoo.com)
Date: Mon Apr 02 2001 - 16:23:50 PDT


Thanks all for responding to my inquiry on the Nyquest
sampling rate. I guess the important take away is that
this sampling theory applies only to a true sine
waveform signal not "Periodic Signals" as I mentioned
in my first mail. I always remembered Fourier series
form my freshman year but did not establish the mental
correlation between "periodic" and "band limited".

 I appreciate all you input.
Adam

--- Ken Cantrell <Ken.Cantrell@srccomp.com> wrote:
> Gaussian, Hamming, and Hanning windows can be used
> to approximate a square
> wave.
>
> -----Original Message-----
> From: owner-si-list@silab.eng.sun.com
> [mailto:owner-si-list@silab.eng.sun.com]On Behalf Of
> Thomas Jackson
> Sent: Monday, April 02, 2001 9:38 AM
> To: 'AA'; Thomas Jackson; si-list@silab.eng.sun.com
> Subject: RE: [SI-LIST] : Nyquist Sampling Rate
>
>
> Adam.
>
> Fourier analysis shows that anything like a
> square-wave, trapezoidal-wave,
> triangular-wave, sawtooth-wave, etc. has frequency
> components going up to
> infinity. Therefore, these signals are not
> band-limited.
>
> The only kinds of signals that can be recovered from
> discrete samples are
> those that can be constructed from a band-limited
> set of sinusoids.
> Luckily, these include or approximate many useful
> real-world signals. The
> highest frequency one of these is a sinewave at 1/2
> the sampling rate.
>
> Tom
>
> -----Original Message-----
> From: AA [mailto:alokbya@yahoo.com]
> Sent: Friday, March 30, 2001 5:43 PM
> To: Thomas Jackson; si-list@silab.eng.sun.com
> Subject: RE: [SI-LIST] : Nyquist Sampling Rate
>
>
> Tom,
> Thanks for the feedback. I know that the sampling
> rate has to be at least twice that hight frequency
> component in the signal. I.e to recover a 60 HZ
> sinwave it needed to be sampled by 120sample/sec
> min.
> How do we know a sine wave produced these samples
> not
> a triangulare wave or other periodic wave form.
>
> Thanks
>
>
> --- Thomas Jackson <tjackson@fmi.fujitsu.com> wrote:
> > Adam,
> >
> > The sampling theorem assumes that you are sampling
> a
> > band-limited signal.
> > Therefore, the highest possible frequency signal
> > through any two points
> > would be a sinewave at 1/2 the sampling rate.
> > Anything else would have
> > frequency components above the Nyquist rate and
> that
> > violates the first
> > assumption.
> >
> > By the way, it should be obvious that the two
> > samples cannot occur at the
> > zero crossings.
> >
> > Tom
> >
> > Thomas L. Jackson, P.E.
> > Staff VLSI Design Engineer
> > Network Access Development
> > Systems Solutions Group
> > FUJITSU MICROELECTRONICS, INC.
> > 3545 North First Street
> > San Jose, CA  95134-1804
> > telephone: (408) 922-9574
> > facsimile: (408) 922-9618
> > http://www.fujitsumicro.com
> >
> >
> > -----Original Message-----
> > From: AA [mailto:alokbya@yahoo.com]
> > Sent: Friday, March 30, 2001 4:43 PM
> > To: si-list@silab.eng.sun.com
> > Subject: [SI-LIST] : Nyquest Sampling Rate
> >
> >
> > DEAR SI list subscribers,
> > Can any one explain to me how you can recover a
> > periodic signal form only 2 samples. I can
> > understand
> > the math but I am having difficulty visualizing
> > this.
> > Draw me any 2 points in the time domain and I can
> > make
> > endless number of periodic signal go through them?
> >
> > I know I am missing a key point but I can quite
> put
> > my
> > finger on it.
> >
> > Your input is very well appreciated.
> >
> > Adam
> >
> >
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> > > tech/recruit/jobreq_optic
> > > si-list@silab.Eng.Sun.COM
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=== message truncated ===

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