After introducing several types of filters in previous articles, this article compares their performance in the time and frequency domain. This is important because the choice of filter is strongly influenced by the domain in which the useful information in your signal is situated…

The moving average is often used for smoothing data in the presence of noise. The simple moving average is not always recognized as the Finite Impulse Response (FIR) filter that it is, while it is actually one of the most common filters in signal processing. Treating it as a filter allows…

I am not a visualization specialist, but I’m convinced that the often used rainbow color map is not well suited for scientific visualization. It might be attractive, but it is not effective. This post mainly introduces diverging color maps as a much better alternative…

As an illustration of some techniques from my series of articles on tomography, I have added a tool that demonstrates basic scanning and reconstruction. Go to the tool. There are several…

This image is the Hubble eXtreme Deep Field (XDF). It was created by combining many images taken between 2002 and 2012 by the Hubble Space Telescope. The total exposure time was 22.5 days (almost 2 million seconds), and the image contains…

Recently, there has been much progress towards proving the twin prime conjecture, one of the great open questions in number theory. There are infinitely many primes, a fact that was already known by the ancient Greek. A short proof, although not the…

I have just posted a major update of my filter design tool. Go to the tool. The new version of the tool allows you to change the sampling rate away from the default of using normalized frequency (but beware of the caveats). Finally, you can also…

If you have ever seen a fireball, which is an unusually bright meteor (or shooting star), then you know that they can be very impressive. But did you also know that reporting your observation can help to further science? Fireballs, and meteors in general, are like…

Frequency response plots are often shown with normalized frequency on the X-axis. This sometimes confuses people. The normalized frequency is computed by dividing the true frequency by the sampling rate. Hence, the sampling rate itself has…

Before you can digitally process an analog (i.e., real-world) signal, you have to convert it to a digital form by sampling it. A very important aspect of this conversion is that you should avoid clipping the original signal. Clipping happens when…