Allen Downey Blog on DSPRelated.com

In Search of The Fourth Wave

Allen Downey — Sat, 25 Sep 2021 17:40:54 +0000

Last year I participated in the first DSP Related online conference, where I presented a short talk called "In Search of The Fourth Wave". It's based on a small mystery I encountered when I was working on Think DSP. As you might know:

A sawtooth wave contains harmonics at integer multiples of the fundamental frequency, and their amplitudes drop off in proportion to...

Autocorrelation and the case of the missing fundamental

Allen Downey — Thu, 21 Jan 2016 19:53:20 +0000

[UPDATED January 25, 2016: One of the examples was broken, also the IPython notebook links now point to nbviewer, where you can hear the examples.]

For sounds with simple harmonic structure, the pitch we perceive is usually the fundamental frequency, even if it is not dominant. For example, here's the spectrum of a half-second recording of a saxophone.

The first three peaks are...

Generating pink noise

Allen Downey — Wed, 20 Jan 2016 20:24:05 +0000

In one of his most famous columns for Scientific American, Martin Gardner wrote about pink noise and its relation to fractal music. The article was based on a 1978 paper by Voss and Clarke, which presents, among other things, a simple algorithm for generating pink noise, also known as 1/f noise.

The fundamental idea of the algorithm is to add up several sequences of...

Amplitude modulation and the sampling theorem

Allen Downey — Fri, 18 Dec 2015 16:24:27 +0000

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done:

Differentiating and integrating discrete signals

Allen Downey — Mon, 14 Dec 2015 15:05:50 +0000

I am back at work on Think DSP, adding a new chapter on differentiation and integration. In the previous chapter (which you can read here) I present Gaussian smoothing, show how smoothing in the time domain corresponds to a low-pass filter in the frequency domain, and present the Convolution Theorem.

In the current chapter, I start with the first difference operation (diff in...

Bayes meets Fourier

Allen Downey — Mon, 26 Oct 2015 19:20:34 +0000

Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died. But recently I have been exploring connections between the Bayes filter and the Fourier transform.

By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state...