Re: square wave harmonic theory (time domain)


"Thomas Magma" <somewhere@xxxxxxxxxxxxxxxxxx> wrote in message
news:wQl7i.241830$aG1.91390@xxxxxxxxxxxx

It would be hard to sample and FFT such as to resolve the 100,000th
harmonic of any waveform.


I was only kind of talking a theoretical ADC. Even though there are ADC's
up in the Giga samples per second, lets talk about a theoretical test with
an ADC that samples at 1Gsps with 24 bit resolution (kick-ass ADC). If I
took a 1 KHz square wave and triggered my ADC on the rising edge of the
pulse...delayed a bit waiting for the transistor to settle (say
200uS)...then took 65536 samples (65uS) of the steady state and did an FFT
on them...what would I see? In the time domain it would appear I was
sampling DC. If the FFT shows high frequencies relating to 1KHz where are
they coming from?

Thomas




The fundamental assumption for the FFT is that the data taken during your
sampling interval repeats from negative infinity to positive infinity. If
you take 65K samples of an unchanging DC level, you will get only DC energy
in the result, (plus all the artifacts from windowing, roundoff, etc.)

So as John pointed out - the harmonics are really there if you sample the
entire 1 kHz wave and it has instantaneous rise/fall times. But if you only
look at a piece of the signal, you get a completely different result.

To minimize the sampling artifacts, make the sample interval an exact
multiple of your waveform's period, so that the "repeating to infinity"
assumption is valid. Since its not usually practical to do that exactly,
window functions are used to reduce the artifacts that will appear when the
FFT algorithm "assumes" its seeing an integral number of periods of an
infinitely repeating waveform.

Steve


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