12bit Sound Reactive Neo-Ring

I've used two ring boards to create a desktop lamp. 

The code has been heavily modified to integrate the new spectrum analyzer mode, in which the LEDs react according to frequency from 20Hz (led at 12 o'clock) to 2kHz ( 11 o'clock). Colors also been improved to perform more changes based on sound rhythm.

You can check the updated code at the github repo.

More info on the project page: https://hackaday.io/project/184291-pilot-sound-reactive-neopixel-lamp

Testing how well performs the board with a more complex operations. 

I've implemented a spectrum analyzer to display the different frequencies on a 0.96" OLED display connected to the Neo-Ring I2C port. Also, LEDs react to that frequencies.

The MCU limitation in terms of memory and power (no FPU) do not allow to use DFT or FFT transformations, even less DSP libraries. Fortunately I found a routine that implements FFT transformations with fixed-point short integers. Also I've used an integer square root implementation from here.

I choose to focus on the most common frequency range with piano music, up to 2kHz, so the audio sampling rate is configured at 4kHz (Nyquist's theorem).

I have to make some adjustments in the source code to integrate it correctly with the rest of the Neo-Ring display modes. When done, I'll update the source code repository.

Comments and suggestions are welcome!