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

From: Mike Jenkins ([email protected])
Date: Mon Apr 09 2001 - 20:21:39 PDT

Larry,

I think we're in "violent agreement". For a sawtooth, the first five
Fourier components are at 1*F, 3*F, 5*F, 7*F and 9*F. That's pretty
close to 10 or 11*F, which is what I presume you mean.

Also, a sawtooth is smoother than, say, a square wave. For a sawtooth
(or any continuous waveform), the coefficients drop off as (1/n)**2.
Hence, that 9*F component is going to be 1/81st as big as the
fundamental,
or about 1% of the sawtooth's amplitude.

Regards,
Mike

Larry Miller wrote:
>
> Mike,
>
> "On a scope screen, one probably could
> not distinguish a perfect sawtooth from a waveform comprised
> of the first, say, five Fourier components."
>
> Yeah, you could. You need at least 10-11 harmonics to be able to turn the
> sharp corners. Even then the distortion for, say, audio frequencies where
> all of the harmonics are within the range of human hearing, is plainly
> audible. Listen to the "sine wave" output of a function generator.
>
> I believe that this is one reason why the "golden ears" guys say they can
> hear the difference between a CD and an analog recording.
>
> Larry Miller
>
> -----Original Message-----
> From: Mike Jenkins [mailto:[email protected]]
> Sent: Tuesday, April 03, 2001 12:54 PM
> To: [email protected]
> Subject: Re: [SI-LIST] : Nyquist Sampling Rate
>
> Thomas Jackson wrote:
> >
> >
> > There are an infinite number of periodic, band-limited signals; they just
> > don't have discontinuities like square, trapezoid, sawtooth, etc. do. In
> > other words, you can't get them directly out of a function generator.
> >
> > Tom
>
> However, with a band-limited signal, you can get ARBITRARILY
> CLOSE approximations. On a scope screen, one probably could
> not distinguish a perfect sawtooth from a waveform comprised
> of the first, say, five Fourier components.
>
> Regards,
> Mike
> >
> > -----Original Message-----
> > From: AA [mailto:[email protected]]
> > Sent: Monday, April 02, 2001 4:24 PM
> > To: Ken Cantrell; Thomas Jackson; [email protected]
> > Subject: RE: [SI-LIST] : Nyquist Sampling Rate
> >
> > 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.
...

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