Signal Processing – Discrete Fourier Transform and Incomplete Fourier Series 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.
 A: If you do not collect at least two samples per period for each and every tone that is in your signal then you will alias that particular oscillation (tone) into a lower frequency and you not only have now a wrong tone, but one that may interfere with a properly sampled tone and one that would have been otherwise correctly represented if not for being aliased (self-jammed) by something else.
A: The DFT treats the data you collect as representing one entire period. It models a periodic function consisting of that data repeated over and over.
If you stop collecting before an entire period has elapsed, the data will model a periodic function consisting of that partial data repeated. It will not have the same shape as the real wave. It will have a higher fundamental frequency.
If you collect fewer data points spread out over the entire period, you will avoid that problem, but create another. As hyportnex said, frequency components that are high enough that you don't have two data points per cycle will be aliased. That is, they will look like a lower frequency. You will be unable to distinguish how much of the signal comes from the high frequency and the aliased low frequency.
