# Re: [SI-LIST] : Nyquist Sampling Rate

From: Shoba Rao ([email protected])
Date: Tue Apr 03 2001 - 13:47:19 PDT

Hi,
My two cents worth..

I dont think your assumption is true. Sampling theory
holds good for all type of signals and not just a true
sine waveform signal which includes aperiodic signals.
For aperiodic signals, since practically you cannot take
infinite number of samples,we assume the signal to be
periodic after N samples.In the fourier domain, you get
a periodic spectra of the fourier transform of your
orginal signal and it can be mathematically proven that
you will be able to recover your signal from the fourier
domain as long as you sample at the Nyquist rate and dont
create aliasing.
Example, if you have a ramp signal, you will be able to
sample at all frequencies and still able to retrieve the
original waveform.

-Shoba.

AA wrote:
>
> 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.
>
> --- Ken Cantrell <[email protected]> wrote:
> > Gaussian, Hamming, and Hanning windows can be used
> > to approximate a square
> > wave.
> >
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]]On Behalf Of
> > Thomas Jackson
> > Sent: Monday, April 02, 2001 9:38 AM
> > To: 'AA'; Thomas Jackson; [email protected]
> > Subject: RE: [SI-LIST] : Nyquist Sampling Rate
> >
> >
> >
> > 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:[email protected]]
> > Sent: Friday, March 30, 2001 5:43 PM
> > To: Thomas Jackson; [email protected]
> > 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 <[email protected]> wrote:
> > >
> > > 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:[email protected]]
> > > Sent: Friday, March 30, 2001 4:43 PM
> > > To: [email protected]
> > > 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.
> > >
> > >
> > >
> > > --- Heinz Blennemann <[email protected]> wrote:
> > > > tech/recruit/jobreq_optic
> > > > [email protected]
> > > > OPENING: Juniper Networks: Electrical/optical
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> > > > optical and electrical technology/component
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> > By
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> === message truncated ===
>
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This archive was generated by hypermail 2b29 : Thu Jun 21 2001 - 10:11:25 PDT