More than a year ago, a friend of mine asked me to write the software for his 3D Spectrum Analyser (3DSA): a device that takes as input an audio signal, and outputs its visualisation on a 3D matrix of leds. If the above description doesn’t quite ring a bell, simply watch the end result in action:
For the hardware fans amongst you, my friend documented the construction process meticulously:
It’s definitely worth watching, e.g. the guy literally built his own fracking PCB from scratch!
I, however, am more a software kinda guy 
In this log, I’ll describe the basic building blocks we needed to get a sound spectrum analyzing algorithm going.
Intro
First things first though, the microprocessor to be programmed was an 80MHz Olimex PIC32, soldered to the PIC32-PINGUINO-OTG development board. (For those who ever tinkered with Arduino boards: it’s the same, only with a faster chip and fewer builtin libraries 
) The Algorithm had to sample the input signal at regular time intervals, convert this signal to the frequency domain, and visualize the detected frequencies on a 16x16x5 LED matrix.
Mathematics
Of course, before writing any code, we had to figure out how to convert input samples to a frequency distribution. This thing is done all the time in signal processing by applying the Discrete Fourier Transform (DFT) to the input signal. Given a signal sampled at a constant frequency, a DFT outputs a set of amplitudes of frequency bands residing in the signal. For example, when your signal mainly consists of the middle C (or Do) tone, a DFT will assign a relatively high amplitude to the frequency band encompassing the corresponding 262 Hz frequency.
However, the human ear perceives sound logarithmically, meaning that a doubling of the frequency of a sound signal is perceived only as a linearly higher tone. In order to compensate for this, we used the Constant Q transform (CQT) instead of the DFT. In short, where a DFT returns amplitudes for frequency bands f-2f-3f-4f-etc., a CQT works with frequency bands f-2f-4f-8f-etc.
So from a theoretical perspective, the algorithm needed for the 3DSA was quite simple: sample the input signal at regular time intervals, apply a CQT calculating amplitudes for 16 frequency bands, and make each of the 16 led columns blink appropriately. Given that the Pinguino development board supported C, we assumed implementing this algorithm wouldn’t be that hard. However, some challenges always pop up
For more detail: Arduino 3D Spectrum Analyser
