Missile, I do not know what that gif is, but it is magic.
Yeah, it's magic!
That's fascinating how....
.... I don't understand A SINGLE thing of what I see and read there. I swear that the only thing I get is that it a gif and some english language under it. Damn. lol
I may try a brief explanation:
Well, the gif shows in one run the core issue of all of digital signal
processing, i.e. of the problem of representing a continuous signal (blue)
with a discrete one (red). Within this example the sampling rate of the blue
signal is held constant. The samples are represented by the red dots. The
white bars are the magnitude spectrum of the discrete/red signal. Basically,
those magnitude tell us how much intensity of a given frequency is in the
digital signal (red). The problem with digital signals is that they have
replicated spectra (see the peaks left and right, initially) induced by the
finite sampling process making the sampled continuous function discrete and
periodic. If one samples a continuous signal with too few samples, said
spectra will get closer together. Upon a certain frequency or a certain low
sample rate, these spectra will start to overlap and as such will influence
each other, i.e. aliasing occurs. This means that the continuous signal can
not be exactly reconstructed from the discrete samples any longer, because,
due to the overlap, the magnitude at each frequency gets mangled up. But when
the replicated spectra don't overlap, the signal can be reconstructed exactly.
But when do they not overlap? That's what Nyquist and Shannon found out a
couple of decades ago. A sufficient condition is when the sample rate with
which we sample the continuous signal (blue) is at least > 2x the highest
frequency of the continuous signal.
The gif above shows how this condition gets violated. Initially, the
replicated spectra are well separated, that means, there are enough sample
points (red dots) with respect to the current frequency of the continuous
signal (blue). But as the frequency of the continuous signal increases, with
the sample rate held fixed, there won't be sufficient samples to keep the
spectra separated from a given point onwards. That's the case when the
frequency of the continuous signal is larger than half the sample rate (the
so-called Nyquist frequency). In this case the spectra start to overlap. In
the animation above the frequency of the continuous signal is increased to an
extend that the replicated spectra go full circle as one can see in the
animation. Hence, while the continuous signal (blue) is at a high frequency,
the sampled version of it (red) is at a lower frequency as the spectrum
clearly shows (center).
One can say that the samples of the high frequency continuous signal include a
copy of the sampled continuous signal at a low frequency. Funny, heh? In the
case shown above you can see a low frequency sine wave (red) while the
continuous signal is at high frequency, hence, aliasing.
This is essentially the reason why one can see low frequency images in high
frequency parts of an image if the images isn't sampled properly or filtered
sufficiently. Now you know from where the artificial circles in a recent
picture of mine come from;
Only the circles with center at the image's midpoint are for real. All the
other ones are due to aliasing of the video signal. One of the tasks of the
Retro Spectral Analyzer is to fine-tune said aliasing. The goal is not to
eliminate it entirely (would defeat the point of being retro to being with),
yet an over-paced version is also not needed.
I can write much more, esp. about the spectrum and how one can see it as a
coordinate vector (functional) of a function in an infinite dimensional vector
space with a basis of periodic functions. But I think I should stop here since
it goes way beyond the thread's subject.
Make that game!
You gave me a good idea making use of it in a game. :+
I'm on no account an expert on the matter, but are we seeing the effect of crossing the Nyquist rate? Anyways, it's fascinating to look at
...
Thanks. Indeed, it's what you said.
Thanks for the flowers, but I didn't do that much. The one to owe is Jean
Baptiste Joseph Fourier (21 March 1768 16 May 1830):
Mr. Fourier, I owe ya!