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

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millwood said:
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
 
Steve Eddy said:


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.
 
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Steve Eddy said:
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.
 
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.
 
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SY said:
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.
 
millwood said:


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.
 
millwood said:



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.
 
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sreten said:
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.
 
millwood said:


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.
 
Oh yes I'm the great pretender.

"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
 

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Re: Oh yes I'm the great pretender.

Fred Dieckmann said:
"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

Having hacked my way through various maths exams doing FT's
(years ago mind you) your presumption "that I'm making it up
as I go along" is entirely based on your lack of FT understanding.

A signal must be made periodic to be FT'd, a single event
is fudged to be a repeated event so you can FT it, the
longer you make the period the more resolution you get
as the longer the period the higher the frequency resolution.

How you apply periodicity to the single event is fundamental
to the accuracy or meaningfulness of the results, the point
is to make the periodicity irrelevant to a meaningful result.

And the basis of the windowing of FFT's.

Not too keen on the "great pretender theme", it would
helpful if "pretenders" also understood hypocracy.

:) sreten.
 
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Graham Maynard said:
However the waveform starts

what waveform? traces, man, traces.

Graham Maynard said:
A filter or amplifier uniquely distorts a first cycle waveform, and we listen to these more than others for our auditory cues.

I find it hard to believe that one can hear distinctively the first cycle of an audio signal. Any scientific evidence to support it?

Graham Maynard said:
My circuit to LineSource does not distort first cycles more than 0.01%, which is especially useful for high audio frequency driving.

is that figure simulated or is it measured? if it simulated, it depends a lot on how the simulator simulates the thing and how you set up the simulator.

Graham Maynard said:
As Fred says, there is a ridiculous amount of background noise here that nobody does anything about, so I'll e-maill you directly.

sometimes it is the foreground noise that is technically troubling.

Graham Maynard said:
When you clean up strings by pulling out the bad attitude stuff, you let the intemperate keyers know that they can get away with writing what they want. There is no reason for them to stop doing it because they know you will wipe their tracks clean.
Your policy is unfair on those who make genuine technical effort.

Is there any way that complaints can be made about individuals ?

Cheers ............ Graham.

this has been a serious discussion of technical issues. What do you want to complain about? I think SE pointed it correctly that if you are looking for people who take your assertations blindly, you are wasting your time.
 
Graham Maynard said:
Is there any way that complaints can be made about individuals?

Yes, there is. At the bottom of each post, next to the "Quote" checkbox is a "Report" button. If you press this button, you will see a form that gives you the chance to make a specific complaint about a post. If the moderator agrees with your complaint it will usually be moved to "Texas", which can be found under "Other" on the home page.

This is quite a useful feature. There are some people that apparently would rather argue than stick to the point of the thread. In my experience it is useless to try and answer these people in a meaningful way as they will continue to argue. Instead, reporting the argumentative post will keep the thread on topic.

The people that like to argue assert that "they have a right to post" or "they were just challenging a technical point" or whatever. But the truth is that they are free to "challenge a technical point" in another thread that they are free to start.

So I would suggest we return to the original point of this thread. I said that he needed +/- 10 volt rails. Graham suggested he needed higher rails, and proceeded to offer his reasons. Even if I disagree, there is something there for me to learn.

And I'm not going to learn squat by arguing with Graham (or anybody else).
 
I think the point here is really that a single AC cycle
has two points of discontinuity, at t = 0 and t = 2pi.

Or only one discontinuity if the sine wave
starts at t=0 and then carries on indefinetely.

At this point, t=0, the slope of the curve is required to
"instantaneously" change implying the hf bandwidth
and stability of the system will determine the "accuracy"
of wave shape reproduction.

In this context the discontinuities of a square or triangular wave
would reveal the same information, HF bandwidth and stability,
as would reproduction of a single pulse.

:) sreten.
 
Dave's 2p / 2c

Hi,
I think there is an issue with computing the FFT of a single sinusoidal cycle as the (most common) algorithms requires the number of sample points to be a power of two. Padding the wave with zeros, to make the length a power of two, will give an unexpected answer but replicating the initial cycle to a give a sample with a large number of cycles will work fine and give the required result (assuming you can line everthing up right and appropriate windowing is used).

Would it not be more valuable to perform this kind of transient test with a delta function (sin(theta) / theta) ?

Dave
 
A common misconception is that people mix up Fourier transform with Fourier analysis.

Fourier analysis is used for periodic signals in order to show their harmonic composition. The result is a discrete specrum (i.e. a line for each harmonic component).

Fourier transform is used for a desired time- sample (not to be mixed-up with the term sample as used when converting a continuous-time signal into a discrete-time one) of an arbitrary signal. The result is a density spectrum.
In this respect Fred is absolutely right, you CAN perform a Fourier transform on an arbitrary part of a sinusoidal. Period. You should just be aware of the differences of what you'd expect to get and what you actually will get.

What most people here want to do with sinusoidals and FFT is performing Fourier ANALYSIS by the use of a Forier transform. Therefore one has to perform the FFT on an integer number of periods of a sinusoidal signal.

Regards

Charles
 
Therefore one has to perform the FFT on an integer number of periods of a sinusoidal signal.

Not really. It is true that if you do an FT on a signal which contains more than one but not an integer number of cycles, you'll get something other than a single line. But the FT is just telling you what's the spectral content of the window you gave it. And the single line will still be predominant, especially if there's a LOT of complete cycles within the window to swamp out the effects of the discontinuity at the beginning and/or end.

Now, there are a few different ways to view what the meaning of the spectral content is when you analyze a signal that has a non-integer number of cycles, but the symmetry of the Fourier integral wrt 2pi rotations leads one to the idea that if you choose a finite window, what you're really doing is forcing the signal to be periodic with a period equal to the window length (NB: I'm using the term "window" here to mean the chosen length of the analyzed signal, not the choice of apodization!). If there are a non-integer number of sinusoidal cycles of a given frequency within the window, there's a discontinuity where the windows "join up", causing the spectrum to be more than just a line. That's the whole reason we do apodization in the first place.
 
Re: Dave's 2p / 2c

DRC said:

Would it not be more valuable to perform this kind of transient test with a delta function (sin(theta) / theta) ?

Dave

Good question, because sin(kx)/x is nothing more than an 'ideal' impulse (google for 'Dirac delta function' for discussion) which has been low-pass filtered (where the filter bandwidth depends on 'k').

This immediately begs the question of what bandwidth you should use. Should this be 20KHz, which is the limit of sine wave audibility, or should it be higher?

If human hearing had special 'rise time detection' apparatus, it might reasonably be higher. Whether or not this is the case is a highly contentious topic...

Cheers
IH
 
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