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Sub: Rigol's DHO800 Oscilloscope (Gibbs Effect & Aliasing Misunderstanding)
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nctnico:
If you are low-pass filtering, you are removing higher harmonics. The ringing on a bandwidth limited square wave are not Gibbs ears. Just less harmonics. Because Gibbs ears are a digital signal processing artefacts from using sin x /x reconstruction, you can't get these on an analog scope because the whole digital signal processing step isn't there.
ebastler:

--- Quote from: nctnico on October 29, 2023, 03:56:03 pm ---If you are low-pass filtering, you are removing higher harmonics. The ringing on a bandwidth limited square wave are not Gibbs ears. Just less harmonics. Because Gibbs ears are a digital signal processing artefacts from using sin x /x reconstruction, you can't get these on an analog scope because the whole digital signal processing step isn't there.

--- End quote ---

My definition of the Gibbs Phenomenon or "Gibbs ears" is the following:

The effect of approximating a signal with sharp jumps (e.g. a square wave) by its partial Fourier series, i.e. by its fundamental frequency and a limited number of harmonics.

Such an approximate representation can be generated in the real world in an additive way (by adding sine functions) or in a subtractive way (by starting with a square wave and removing higher harmonics via low-pass filtering). In either case, the resulting output is an example of the Gibbs phenomenon in my book, and will show the characteristic "ears".

Your definition of the Gibbs Phenomenon seems to be different from mine. Could you state what it is, and where you got it from?
nctnico:
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.
Mechatrommer:

--- Quote from: nctnico on October 29, 2023, 03:56:03 pm ---If you are low-pass filtering, you are removing higher harmonics. The ringing on a bandwidth limited square wave are not Gibbs ears. Just less harmonics. Because Gibbs ears are a digital signal processing artefacts from using sin x /x reconstruction, you can't get these on an analog scope because the whole digital signal processing step isn't there.

--- End quote ---
tracing back history, it came from Fourier Series itself Jean-Baptiste Joseph Fourier (1768–1830), and then the Gibbs Phenomenon discovered by Henry Wilbraham (25 July 1825 – 13 February 1883)... so, since i guess Sinc is using some of Fourier derivative, so the effect as well... Sinc is too math complicated for me, but i have FFT library that can easily produce this effect by band limiting in digital (FFT) and do the inverse FFT. i dont care whether if its a "conceptual", "theoretical", or "mathematical" property, as long as we can mimick it in reality, then we call it that... just as singularity, we call black hole is a singularity, not because its the truth singularity, but thats a reality we dont understand about where all the mathematical formulations, scientifical theory and logics collapse. i dont have time with this literalism
Mechatrommer:

--- 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...
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