Talk:Nyquist–Shannon sampling theorem

Article is too technical

The articles is not written to the "Wikipedia:Make technical articles understandable" guidelines. Nowhere in the article does it plainly state the concept that a digital signal should be sampled at twice the resolution of the original source to achieve quality reproduction. With the theorem's most famous use being the 44.1kHz/16bit CD-quality resolution standard, there's no mention of Phillips/Sony using the Nyquist-Shannon theorem to reach that seemingly arbitrary resolution.

DracheMitch (talk) 05:22, 11 September 2019 (UTC)

I think that your assertion is broken on a few levels;

• It's written elsewhere that the sampling rate used for digital audio sampling at the time of the creation of the CD-DA format was 48,000 samples per second.
• You conflate "rate" with "resolution".
• The statement which you deem as "famous" is often over-simplified and misunderstood. It's a realisation that there's an obvious limit. Simply re-expressed, it's that there's no chance at all that a sine wave[1] sampled two times per cycle can be reproduced accurately. I'd assert that it's more akin to the event horizon in cosmology and the relativistic physics of supermassive objects.
• Sony already had a tape format which used the lower 44.1ks/s rate and pushed for alignment with that.

[1] I say "sine wave" here as it's the minimum unit of information at the extreme upper limit - anything which is not a sine wave has components at frequencies higher than the fundamental and therefore not relevant.

Anything written is understandable.

Is the article not understandable?

It's not likely that my writings here would be allowed in the article, as what I write here counts as "thought" and as not "reference". Qfissler (talk) 21:38, 10 March 2022 (UTC)

I disagree in one respect and agree in another. First, the theorem actually applies to any band-limited spectrum, where supp X ⊆ [f₋,f₊] where 0 < f₊ - f₋ ≤ 1/T, not just to the special case where f_± = ±½ 1/T, nor even just to the further specialization where x is real and X is redundant across f = 0. The Nyquist condition is a separate issue that shouldn't be mixed in with this. Second, I agree in one respect that the derivations don't get to the essence of the matter: the distributional identity ∑_{n∈ℤ} δ(x - n) = ∑_{k∈ℤ} exp(2πikx) that also underlies the Poisson summation formula. It should either be used for the derivation (and possibly also retrofit into the Poisson summation formula article) or else at least noted and shown how equation 1 can be expressed in terms of it (e.g. using properties such as T δ(Tx) = δ(x) for T > 0). It's a pretty important fundamental that crops up in engineering texts, as well.

Small Mistake in Introduction

The last sentence in the Intro says that "usually followed by an "anti-aliasing filter" to clean up spurious high-frequency content."

This is not quite right. The "anti-aliasing" filter goes at the beginning of the process between the analog signal and the ADC. The filter at the end of the process is a low-pass filter called the "reconstruction filter". For more details, see http://www.dspguide.com/ch3/4.htm — Preceding unsigned comment added by 154.20.208.115 (talk) 03:54, 6 October 2019 (UTC)

Historical background

Looking at Nyquist–Shannon_sampling_theorem#Shannon's_original_proof, Shannon was just one mathematical step (and the obvious assertion of Fourier series periodicity) away from writing the Poisson Summation Formula for his specific case (T = 1/2B). Instead he chose to describe that step in the briefest possible text, which makes it look like he was trying to avoid drawing attention to Poisson's earlier and more general discovery. Perhaps Shannon's actual contribution was not his proof, but highlighting the relevance of Poisson's work to contemporary DSP. I mention this because of all the other 20th century mathematicians we mention who have an arguable claim to the discovery. But Poisson was a century ahead of them all.
--Bob K (talk) 17:00, 10 October 2019 (UTC)

Interesting, assuming more editors agree with "Poisson was a century ahead of them all" I think this would be a good addition to the article. BernardoSulzbach (talk) 23:53, 13 October 2019 (UTC)

I think the confusion in naming comes from conflating different areas of study. Nyquist’s work was specifically aimed at determining what sample rate would be needed to transmit analog information in a digital medium. So to Electrical Engineers or anyone studying digital audio or video equipment and technology “Nyquist theorem” makes the most sense. A mathematician may see it differently because they see it as a broader mathematical problem. 75.100.4.194 (talk) 08:18, 12 June 2024 (UTC)

is it true that smartphone cameras "remove aliasing with a digital filter"

In the section 'Application to multivariable signals and images' talking about digital cameras, there is this:

Instead of requiring an optical filter, the graphics processing unit of smartphone cameras performs digital signal processing to remove aliasing with a digital filter.

— article

This is not my area, but is that actually true? I thought the main point of Nyquist-Shannon was that the analog signal has to be bandwidth-limited before being digitized, to avoid aliased signals in the digital representation, because aliased signals generally can't be 'filtered out' of a digitized signal, because they don't look any different than un-aliased signals. Or is smartphone digital photography one of the special cases mentioned in the article's 1st section?

Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known

— section 1, para 2

I feel that 'remove aliasing with a digital filter' needs at least a word or two of explanation. Surely with a smartphone camera they aren't just oversampling by 2x or 4x?? Spike0xff (talk) 00:25, 11 September 2021 (UTC)