Fourier transforms (split from 25W class A into 1 ohm resistive load)

[Steve Eddy]

Originally posted by millwood
I am not sure what you meant and mean by "first cycle distortion" as certainly it is not possible to do an fft using just the first cycle waveform.

Why is it impossible? You can do an FFT on a single cycle, yes?

I think what Graham seems to be overlooking is that within that first cycle there will be frequency components other than the fundamental frequency of the sinusoid.

jcx alluded to this previously when he asked:

hi graham, I’m having a hard time seeing "1st cycle distortion" as anything more than a sneaky way to demand “ridiculous” bandwidth, perhaps you have a methodology that doesn't include the frequency components from the discontinuity at t = 0?

So where do we stop then? the longer we sample the waveform for fft, the less effect we get for the first cycle. I guess you will have to define "first cycle distortion" better for us.

Yes.

se

[sreten]

Originally posted by Steve Eddy


Why is it impossible? You can do an FFT on a single cycle, yes?

se

You can do an FFT on a single cycle but the implied start/stop
conditions would add copious higher order harmonics to the
result rendering it essentially meaningless.

EDIT : just to be clear an FFT assumes a repeating waveform,
so for a "single" AC cycle the majority of the period is flat,
i.e. zero with a single AC cycle in the middle.
The FTT would be of a repetitive spaced "single AC cycle".

It should be noted that a single AC cycle O up to peak back
through O down to trough and then back to O has totally
unrealistic bandwidth requirements for its start and stop.

sreten.

[millwood]

Originally posted by Steve Eddy
Why is it impossible? You can do an FFT on a single cycle, yes?
se

by "single cycle", I meant one 360 degree cycle (from zero to peak, to the trough and back to zero).

the number of "foundamental" frequencies in an FFT analysis depends on how many cycles you go through. The more cycles, the more information the waveform contains and the further out you can go. I don't recall the exact formula now but intuitively that's how I remember it.

So if all you have is a one 360 degree cycle, you wouldn't have sufficient data for fft.

[SY]

No, you absolutely DO have enough info for an FFT. If you treat the waveform as periodic, but terminating at zero and 2pi, then you've satisfied the Nyquist critereon and you'll have a single line in the frequency domain. If you take the window as something greater than zero->2pi, you'll have that line plus a whole bunch of other garbage.

[millwood]

Originally posted by SY
If you treat the waveform as periodic,

I think that was the assumption I wasn't willing to make: the waveform will repeat itself indefinitely.

Sure, once you have that assumption, you have enough information for FFT til infinity.

But what if you don't?

In the case of Graham's questioning, I don't think it makes sense to say that the amp will repeat its behaviors in the first cycle until infinity.

[sreten]

Originally posted by millwood


by "single cycle", I meant one 360 degree cycle (from zero to peak, to the trough and back to zero).

the number of "foundamental" frequencies in an FFT analysis depends on how many cycles you go through. The more cycles, the more information the waveform contains and the further out you can go. I don't recall the exact formula now but intuitively that's how I remember it.

So if all you have is a one 360 degree cycle, you wouldn't have sufficient data for fft.

Sorry but you've either got this wrong, or misunderstood.

A FFT presumes you have a infinitely repeating waveform,
that each period is identical and the ends of the period are
at the same point and continuous.

so to emulate a single cycle :

EDIT : just to be clear an FFT assumes a repeating waveform,so for a "single" AC cycle the majority of the period is flat, i.e. zero with a single AC cycle in the middle. The FTT would be of a repetitive spaced "single AC cycle".

sreten.

[SY]

Originally posted by millwood



I think that was the assumption I wasn't willing to make: the waveform will repeat itself indefinitely.

Sure, once you have that assumption, you have enough information for FFT til infinity.

But what if you don't?

Well, even if you don't, the periodicity is taken to be the sampling length. So one way or another, you're forced into some sort of periodicity.

[millwood]

Originally posted by sreten
A FFT presumes you have a infinitely repeating waveform,
that each period is identical and the ends of the period are
at the same point and continuous.

sreten.

that's only true if you are doing fft in math. in reality, fft is done via sampling of a finite time series where you don't need the waveform to be infitely long.

[sreten]

Originally posted by millwood


I think that was the assumption I wasn't willing to make: the waveform will repeat itself indefinitely.

Sure, once you have that assumption, you have enough information for FFT til infinity.

But what if you don't?

a single cycle every 100 years is eminently calculable but very
hard work for precision. I'd say less than 1Hz repeating can
be effectively treated as a single event, probably higher.

The point with FFT is you have to pretend the signal repeats,
even if its a one off event, but the converse is you can repeat
that one event theorectically since time began until it ends.

sreten.

[Fred Dieckmann]

"The point with FFT is you have to pretend the signal repeats,
even if its a one off event, but the converse is you can repeat
that one event theorectically since time began until it ends."


Is there anybody in this thread that is not just making all this up as they go along. I am beginning to wonder if any one here knows what a Fourier Transform is at all, that being, a tool to look at the frequency spectrum for a given time domain signal. It doesn't have to be a periodic signal in the time domain.

As close to layman's terms as I have found so far:

http://www.siasoft.com/pdf/FFT-Fundamentals.pdf