Re: square wave harmonic theory (time domain)

On Wed, 30 May 2007 22:02:43 GMT, "Thomas Magma"
<somewhere@xxxxxxxxxxxxxxxxxx> wrote:

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.


So now I'm really confused, are you saying that during certain times of a
square wave there is no harmonic content? Would that not imply that the high
frequency harmonics are stronger at certain instances of time compared to
others?

A square wave is forever. If you examine a little time slice of a
square wave, it's not a square wave... it's a rise, or a fall, or DC.

John


.

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