Yes, you can do symbolic math in Python! The library to take a look at is SymPy. This article is not a SymPy tutorial, as I only want to walk you through some examples to show you the kinds of things that it can do. A good place to start… read more
Turtle graphics are a way of drawing where you control a cursor, known as the “turtle”, by instructing it how to move. For example, you tell the turtle to move forward over a certain distance, drawing a line on your screen in the process, then… read more
I’d like to add another trick to your digital filter toolbox: when you apply any filter in both directions on your input signal, the combined filtering operation is zero phase. As you know from… read more
To close the series of articles on how to compute fractals using NumPy array operations, I want to show you one more thing: how to create animated GIFs from those NumPy arrays. The first point to make is that… read more
As a variation on the Mandelbrot fractal that I’ve computed before using NumPy array operations, I’d like to show you a few Julia fractals with some color added. I’ll concentrate on the Julia sets that are generated using the same quadratic polynomial that is used to… read more
If you use NumPy for numerical computations, which I recommend if you program in Python, one of the key things to do is to process entire arrays in one go as much as possible (this is also true for MATLAB). Using these so-called vectorized operations makes sure that… read more
Say that you have implemented a low-pass FIR filter with the correct cut-off frequency and transition band, but that you are not quite happy with the suppression of frequencies in the stop band. A straightforward trick to put in your toolbox is that you can double the suppression by… read more
Do you know what a quine is? Here is an example in Python… read more
The article Why use Symmetrical FIR Filters with an Odd Length? mentiones that symmetrical FIR filters are linear phase. In this follow-up article, I simply want to show you what the phase response of these filters actually looks like… read more
In my articles on filter design I mostly focus on a rather specific subset of all possible filters, namely symmetrical FIR filters with an odd number of coefficients. Each of these properties (1. FIR, 2. symmetrical, and 3. an odd number of coefficients) was chosen for… read more
