Discrete Fourier Transform and Incomplete Fourier Series

Question

I'm working on a paper where I'm collecting sound pressure data from a chord's wave and trying to create a frequency spectrum to find the individual frequencies that make up the chord.

However, I can't process too many data points (software). To ensure a sampling rate higher than twice the highest note, I can't collect SPL data for the entire period of the chord's wave.

Would the DFT still work and pick up the individual frequencies on the frequency spectrum if not the entire chord's period is collected?

Thanks.

Answer 1

However, I can't process too many data points (software).

Why not? That would be unusual limit. By today's standard that requires very little memory and CPU.

To ensure a sampling rate higher than twice the highest note,

Careful here. A note typically consists of a harmonic line spectrum and NOT a single frequency. You need capture enough harmonics to get the pitch from the harmonic spacing. The fundamental can be weak or missing entirely.

Would the DFT still work and pick up the individual frequencies on the frequency spectrum if not the entire chord's period is collected?

Unlikely. The FFT isn't a great tool for pitch detection in the first place. It's frequency resolution is given by $\Delta f = f_s/N$ where $f_s$ is the sample rate and $N$ the FFT length. Short FFTs have very poor resolution.