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Sub: Rigol's DHO800 Oscilloscope (Gibbs Effect & Aliasing Misunderstanding)
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nctnico:

--- Quote from: ebastler on October 29, 2023, 04:19:46 pm ---
--- Quote from: nctnico on October 29, 2023, 04:12:12 pm ---Read the Wikipedia article carefully. It says that a square wave can not be constructed from a fourier series because a square wave is a discontinuous function. As a result you get artificial ringing near the edges.

--- End quote ---

 ???

So how is this different from what I said? A square wave cannot be exctly represented as a finite Fourier series. If you truncate the series somewhere, you will see the Gibbs effect. The ringing near the edges is the Gibbs effect.

--- End quote ---
It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.
ebastler:

--- Quote from: nctnico on October 29, 2023, 04:25:41 pm ---It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.

--- End quote ---

I keep reading "that is not the Gibbs effect, because that is not the Gibbs effect" from you.
Please state your definition, thanks!

And the statement in bold is just plain wrong, under any definition, sorry. Look at the limit for pushing the number of Fourier components towards infinity, and measure e.g. an RMS deviation between the square wave and its Fourier series. What would you claim the limiting value is?
Mechatrommer:

--- Quote from: nctnico on October 29, 2023, 04:19:19 pm ---
--- Quote from: Mechatrommer on October 29, 2023, 04:17:25 pm ---
--- Quote from: nctnico on October 29, 2023, 04:12:12 pm ---Read the Wikipedia article carefully. It says that a square wave can not be constructed from a fourier series because a square wave is a discontinuous function. As a result you get artificial ringing near the edges. The discontinuity gets you artificial pre-ringing when using sin x /x reconstruction.

--- End quote ---
yes you can get perfect square with fourier series, except the order N = infinity...

--- End quote ---
Nope.
--- End quote ---
there are differences between theoretical science and applied science ;) applied scientists try to make theoritical applicable. one of it is FFT. knowing there are limitations what a real world can do, or what we can achieve, we know where to stop as "good enough". theoritical by itself is useless if it cannot be applied. imho ymmv.
wasedadoc:

--- Quote from: nctnico on October 29, 2023, 01:55:57 pm ---Nope. Your scope is showing the real signal. Not 'virtual' Gibbs ears. The dead-giveaway is that the signal doesn't change between vector, dot and sin x /x mode.

--- End quote ---
That is not a dead-giveaway.  The square wave frequency is 100kHz. The sample rate is 250MHz.  That means 2500 samples for every period.  There would not be any visible change between modes.
wasedadoc:

--- Quote from: nctnico on October 29, 2023, 04:25:41 pm ---
--- Quote from: ebastler on October 29, 2023, 04:19:46 pm ---
--- Quote from: nctnico on October 29, 2023, 04:12:12 pm ---Read the Wikipedia article carefully. It says that a square wave can not be constructed from a fourier series because a square wave is a discontinuous function. As a result you get artificial ringing near the edges.

--- End quote ---

 ???

So how is this different from what I said? A square wave cannot be exctly represented as a finite Fourier series. If you truncate the series somewhere, you will see the Gibbs effect. The ringing near the edges is the Gibbs effect.

--- End quote ---
It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.

--- End quote ---
And how did the mathematicians produce the Gibbs ears?  They added a limited number of harmonics.  Are you disputing that is not "bandwidth limited"?
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