What is a Hadamard Matrix?

A Hadamard matrix is a matrix with all elements equal to \(+1\) or \(-1\), and for which the rows are mutually orthogonal. If you pick two rows from the matrix and write it as vectors \(\bf x\) and \(\bf y\), then these are orthogonal if… read more

Submitted on 6 December 2017

Jerk

What is jerk? Jerk is to acceleration as acceleration is to velocity. And, acceleration is to velocity as velocity is to position. So let’s start there. The instantaneous velocity at which you travel tells you… read more

Submitted on 20 November 2017

The Birthday Paradox

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… read more

Submitted on 5 March 2017

Exponentiation by Squaring

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… read more

Submitted on 12 February 2017

Randomness Explains Flat Tire Anecdotes Perfectly Well

Figure 2. First five simulated periods of 30 years.

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… read more

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Submitted on 22 January 2017

How to Create a Configurable Filter Using a Kaiser Window

Figure 3. Frequency response of a low-pass filter with a Kaiser window; A=60.

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… read more

Submitted on 26 December 2016

Some Mathematics Behind "Catching Them All"

Pokémon Go logo

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… read more

Submitted on 28 September 2016

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