## How is the Size of A4 Paper Determined?

The most common size of ISO A series paper is A4, of which the exact size is 210 × 297 mm. How is that size determined? Amazingly, you can exactly compute all the sizes of the A series sheets from the following two simple rules… read more

## What is a Spectrogram?

A *spectrogram* is a graph that shows the evolution of the *spectrum* (the frequency contents) of a signal over time. Often, the frequency is on the vertical axis and time is on the horizontal axis. A spectrogram is computed by “chopping up” the signal into chunks and computing… read more

## Naive Square Wave

After introducing finite-bandwidth square waves in previous articles, I’ll now describe what happens if you follow the naive approach, and just alternate sequences of 1’s and −1’s. As you might expect after reading the previous articles, there are several problems with this. The first problem is that the naive square wave is… read more

## Finite-Bandwidth Square Wave in Samples

After introducing the finite-bandwidth square wave in a previous article, I’ll show in this one how such a square wave looks in a digital system, so in sampled form. The figure below shows one period of a square wave of 1 kHz, sampled at 44.1 kHz, a widely used… read more

## Finite-Bandwidth Square Wave

How would you produce a *square wave* on a digital system? At first sight, this seems completely trivial. You might think that you could just alternate a series of +1 values with a series of −1 values and be done with it. Well, it doesn’t work like that. An ideal square wave needs infinite bandwith, so creating one is… read more

## Color PSFs

After computing The PSF of a Pinhole Camera and showing Some Wacky Pinholes and Their PSF in previous articles, the next step towards ever more realistic PSFs is adding color. A DSLR camera has detector pixels that are sensitive to red, green, and blue, and, since the size of the PSF depends on… read more

## Some Wacky Pinholes and Their PSF

After simulating a round pinhole and showing the resulting point spread function (PSF) both far away (equivalent to the Airy disk) and close by (resulting in a realistic PSF for a DSLR pinhole camera) in The PSF of a Pinhole Camera, I show the PSFs of some more wacky pinholes here… read more

## Gorsaf Heddlu

A well-labeled police station (gorsaf heddlu in Welsh) in Llangollen, Wales. read more

## The PSF of a Pinhole Camera

After introducing the Airy pattern in The Perfect Camera, I will show in this article how the PSF of a pinhole camera looks. A camera with a classical lens focuses the image that would be at infinity on the detector, which means that you actually get (approximately) the Airy pattern as the image of a point source there. This is not true for a pinhole camera, so… read more