This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. For the specific case of a filter, the frequency response tells you exactly how each frequency is altered. The example code is…

How many people do you need before the probability that two of them have the same birthday is 50%? The answer to this question is, amazingly, 23. This surprising result is known as the birthday paradox. The word paradox is used here in the sense that…

In this article, I present the simple idea of exponentiation by squaring. This idea saves computation time in determining the value of large integer powers by “splitting” the exponentiation in a clever way into a series of squaring operations. The technique is based on the fact that…

Flat tires are random events. However, it seems that the human mind expects random events to be more regular than they actually are. This intuition on randomness might lead to the feeling that your own experience is somehow unexpected or strange, with anecdotes such as “my uncle seems to never have any flats, but my sister had three in the last year alone”. This is related…

This article is a wrap-up of what happened on TomRoelandts.com in 2016.

This article explains how to create a windowed-sinc filter with a Kaiser (or Kaiser-Bessel) window. The windowed-sinc filters in previous articles typically had two parameters, the cutoff frequency and the transition bandwidth (or rolloff). With a Kaiser window, there is a third input parameter, the ripple. For the specific case of the Kaiser window, the same…

This article contains more detailed information on setting the transition bandwidth (or roll-off) from How to Create a Simple Low-Pass Filter. That article suggest to use, as the filter length N, an odd number close to 4/b, where b is the required transition bandwidth. This is a good basic rule. However, in…

Mathematics is everywhere. In this article, I present some of the mathematics behind “Catching Them All”. Say that a rare Pokémon pops up in your Sightings, and that you walk in a straight line until it disappears again. What have you then learned about the position of that Pokémon? Well, since the…

This is part three of an article that describes the signal path of a radio meteor. The next step is sampling. At the point of sampling, there is a difference between a real-world BRAMS system and the simulation that produced the illustrations in this series of articles. In the real system…

This is part two of an article that describes the signal path of a radio meteor. At the antenna of the receiver, the reflected signal is combined with a (much smaller) directly received signal. At first sight this might seem unimportant, since the amplitude of the direct component is typically much less than…