ppppenguin wrote:Gary raises several interesting points.
Taking the last one first, I really don't think that sampling theory can be equated with Heisenberg's uncertainty principle. Sampling theory, Fourier, Nyquist etc all emerge naturally from the maths while the uncertainty principle is related to measurement and the presence of an observer. Leads us into difficult metaphysics very quickly.
Er no,
"Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems, that is, without changing something in a system. Heisenberg offered such an observer effect at the quantum level as a physical "explanation" of quantum uncertainty. It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems."
In relation to filter design:
"As stated in the uncertainty principle, the product of the width of the frequency function and the width of the impulse response cannot be smaller than a specific constant. This implies that if a specific frequency function is requested, corresponding to a specific frequency width, the minimum width of the filter in the signal domain is set. Vice versa, if the maximum width of the response is given, this determines the smallest possible width in the frequency. This is a typical example of contradictory requirements where the filter design process may try to find a useful compromise."
The Uncertainty Principle is a mathematical concept:
- uncertainty.JPG (12.08 KiB) Viewed 13910 times
Never mind, that was not taught at Uni when I went either.
No, it doesn't matter what the data is, sound, video, population statistics, telemetry, it is all the same, if the data can be represented as a function, it can be represented by sums simpler trigonometric functions - this is called Fourier Analysis and is fundamental to any type of signal processing.
ppppenguin wrote:I think there are some functions that don't work properly with Fourier analysis. My maths isn't good enough to demonstrate this but I think that artificial sequences such as infinitely sharp transitions from white to black can fool the system. And give horrible ringing if you try to filter them other than gently.
Well the data or signal must be periodic, but any set of data can be windowed to appear periodic. Whether that is appropriate or not depends on what you are trying to achieve.
I am struggling to come up with anything that can't be the subject of Fourier Analysis but the number of possibilities is infinite. As far as I am aware the topic is mathematically controversial. Suffice it to say, as an electrical engineer I have yet to come up with anything in my domain that cannot be analysed.
But yes, what you say is perfectly correct, and is indeed, the source of the Gibb's Phenomenon I remarked upon earlier. That transition from "white to black" is the "discontinuity" I refer to - because, as a signal it requires an infinitely steep slope, or zero rise time to instantaneously go from minimum to maximum.
I didn't mention this before as I thought it obvious but maybe it isn't, but the ringing that Andrew has demonstrated above depends very much on the picture content - if the picture he shows above had low greyscale values above the sync pulse the ringing would not be as severe at that point.
ppppenguin wrote:Quantising (number of bits) is a completely separate argument to sampling.
I am not sure why you are bringing that up, I certainly didn't (at least intentionally) - If you are referring to the 0-255 values that Andrew brought up then consider those as a mapping of 0 to 1.0.
ppppenguin wrote: Fourier analysis doesn't involve quantising. If you don't have enough bits then you'll get additional errors above any caused by aliasing but that's not a problem in any well designed system. By proper application of dither any quantising errors can be turned into noise, thus avoiding the posterisation and banding effects you sometimes see. If you don't have enough bits in a filter calculation you can sometimes get overflow or underflow which will cause unexpected additional errors. The output of a filter can always be rounded to any desired number of bits. If done correctly this gives the usual tradeoff between number of bits and noise.
Indeed, there are many aspects of signal processing that need to be taken into account, but we are talking about ringing here so I am not exactly sure of your point unless it was to add another source of error. (LOL I meant "draw attention to another source of error").
ppppenguin wrote:As an aside I once experimented with 1 bit video. Looked evil on monochrome pictures but PAL colour subcarrier was an effective dither signal so coloured parts of the picture looked much better.
Dithering a 1 bit signal is something I need to get my head around. LOL