Definition of 'aliasing' (in signal processing)

[KarlGauss]

In this Wiki article on aliasing, the following statement is made:

@Wiki on Aliasing

. . . aliasing refers to an effect that causes different continuous signals to become indistinguishable (or aliases of one another) when sampled.

Fair enough.

But then, two sentences later, we find this:

@two sentences later in Wiki on Aliasing

When we view a digital photograph, the reconstruction (interpolation) is performed by a display or printer device, and by our eyes and our brain. If the reconstructed image differs from the original image, we are seeing an alias.

Now hold on a minute! Is that not the opposite of we’re told in the first quote above? The first quote says that if signals become indistinguishable, that’s aliasing. But the second quote is saying that if the image (i.e. signal) differs from the original, then that’s an alias.

Can someone set me straight, please? Is it me or Wiki (or both) that’s mixed up?

Thanks!

[David_Simmons]

Suppose we have a sampling frequency of 1 and we sample a a signal having a frequency of 0.1. We will see a reasonably true representation of the original signal. That is, our sampling process will give us an output signal of frequency 0.1

Now suppose our signal has a frequency of 1.1. Sampled at a frequency of 1 that will also give us an output frequency of 0.1. The output frequency is different from the input frequency and it is indistinguishable from the case where the input frequency is 0.1.

[David_Simmons]

I think what they are saying is that if your cameral has a resolution of 1000 pixels/inch in the horizontal and the scence only changes at a max rate of 100/ inch you get a true image.

However if the scene changes at a rate of 1100/ inch you see an image that changes at a max rate of 100/inch. The scene you see is an alias of a scene that changes at 100/inch and it is different from the scene that was photographed.

[Princhester]

There’s no contradiction:

Input = A, output = C
Input = B, output = C

The first sentence of Wiki that you quote is saying that inaccurate sampling can lead to two different inputs (A&B) becoming indistinguishable. The second sentence is pointing out that this can mean that your output is very different to your inputs. Particularly if the difference between A & B is crucial to how we perceive the overall thing.

[Princhester]

In other words aliasing can refer to

• two different inputs becoming indistinguishable in terms of outputs (the cause of the problem) and also to

• the way this can cause an overall output to be perceived very differently to the inputs (the effect of the problem).

[KarlGauss]

Ah! A very helpful way of looking at it (and phrasing it). Much obliged.

Thanks to both of you for your efforts.

Now, I’m going to (try to) let it become intuitive.