I had thought of a ‘pixel’ as the smallest unit of digital space, like a tiny square, and that digitial images are made of up such units. This article says it is not that simple and that it is related to Fourier transforms, in which any wave form can be decomposed into the sum of sinusoidal waves of different frequencies.
Perhaps the most unexpected person in this story – at least for readers in the United States – is Vladimir Kotelnikov, the man who turned Fourier’s idea into the pixel.
Early in his career, Kotelnikov showed how to represent a picture with what we now call pixels. His beautiful and astonishing sampling theorem, published in 1933, is the foundation of the modern picture world.
A pixel exists only at a point. It’s zero-dimensional (0D), with no extent. You can’t see a pixel.
What devices do is ‘spread’ those pixels to create an image.
You carry pixels around in your cellphone, say, stored in picture files. You cannot see the pixels. To see them, you ask for a picture file to be displayed. Typically, you ‘click on it’. Because of the astounding speed of today’s computers, this seems to happen instantaneously. The digital pixels are sent to the display device, which spreads them with the little glowing spots on the display’s screen. The act of display is the process I just described and diagrammed. Those glowing spots are actual pixel-spreaders at work.
Many people call these spots pixels – a very common error. Pixels are digital, separated, spiky things, and are invisible. The little glowing spots are analogue, overlapped, smooth things, and are visible. I suggest we call each a ‘display element’ to distinguish it from a ‘picture element’ (which is what the word ‘pixel’ abbreviates). Display elements and pixels are fundamentally different kinds of things. Display elements vary from manufacturer to manufacturer, from display to display, and over time as display technologies evolve. But pixels are universal, the same everywhere – even on Mars – and across the decades.
I have not invoked a little square even once in this discussion. A pixel – an invisible 0D point – cannot be a square, and the little glowing spot of light from a display device generally isn’t either. It can be, but only if the spreader is a hard-edged box – an unnatural shape, a mesa with a square footprint. A square mesa is a jarringly crude approximation to the gentle hillock spreader supported by the sampling theorem.
So why do so many people think that pixels are little squares? The answer is simple: apps and displays have fooled us for decades with a cheap and dirty trick. To ‘zoom in’ by a factor of 20, say, they replace each pixel with a 20-by-20 square array of copies of that pixel, and display the result. It’s a picture of 400 (spread) pixels of the same colour arranged in a square. It looks like a little square – what a surprise. It’s definitely not a picture of the original pixel made 20 times larger.
I cannot effectively summarize the long article because it is quite dense and contains a lot of images but I encourage interested people to follow the link.