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12th April 2004, 08:25 PM  #1  
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Join Date: Sep 2002
Location: Sacramento, CA

Quote:
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? Quote:
se 

12th April 2004, 08:36 PM  #2  
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Join Date: Nov 2003
Location: Brighton UK

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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. 

12th April 2004, 09:29 PM  #3  
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Join Date: Apr 2003
Location: US

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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. 

12th April 2004, 09:50 PM  #4 
diyAudio Moderator

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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12th April 2004, 09:54 PM  #5  
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Location: US

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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. 

12th April 2004, 10:01 PM  #6  
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Join Date: Nov 2003
Location: Brighton UK

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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 : Quote:


12th April 2004, 10:07 PM  #7  
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"Pity, wrath, heroism, filled them, but the power of putting two and two together was annihilated." EM Forster 

12th April 2004, 10:11 PM  #8  
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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. 

12th April 2004, 10:21 PM  #9  
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Location: Brighton UK

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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. 

12th April 2004, 11:08 PM  #10 
diyAudio Retiree
Join Date: Oct 2002
Location: Spain or the pueblo of Los Angeles

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/FFTFundamentals.pdf 
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