How to resolve frequency from PCM samples

Question

I'd like to build a an audio visualizer display using led strips to be used at parties. Building the display and programming the rendering engine is fairly straightforward, but I don't have any experience in signal processing, aside from rendering PCM samples.

The primary feature I'd like to implement would be animation driven by audible frequency. To keep things super simple and get the hang of it, I'd like to start by simply rendering a color according to audible frequency of the input signal (e.g. the highest audible frequency would be rendered as white).

I understand that reading input samples as PCM gives me the amplitude of air pressure (intensity) with respect to time and that using a Fourier transform outputs the signal as intensity with respect to frequency. But from there I'm lost as to how to resolve the actual frequency.

Would the numeric frequency need to be resolved as the inverse transform of the of the Fourier transform (e.g. the intensity is the argument and the frequency is the result)?

I understand there are different types of Fourier transforms that are suitable for different purposes. Which is useful for such an application?

Answer 1

You can transform the samples from time domain to frequency domain using DFT or FFT. It outputs frequencies and their intensities. Actually you get a set of frequencies not just one. Based on that LED strips can be lit. See DFT spectrum tracer

Answer 2

"The frequency", as in a single numeric audio frequency spectrum value, does not exist for almost all sounds. That's why an FFT gives you all N/2 frequency bins of the full audio spectrum, up to half the sample rate, with a resolution determined by the length of the FFT.