My colleague and I are trying to learn stuff that is way above our pay grade. We are curious about the nature of the FFT. We realize that we will most likely not understand the inner workings of the FFT but would like to understand the data that is input and output from the algorithm.
I should probably mention that we are using MathDotNet's Numerics library for .net. (This is not a question about .net, but this info may be helpful for context)
Say we have a series of coordinates and we wish to run an FFT to extract the various frequencies hidden within. The particular FFT function we are using expects a series of Complex (polar) values so we enter them as follows:
say the sample point = (10,5) therefor the complex value we input is (10 ∠0)
Why is the ∠ = 0? We have read that in the context of "real ffts" the imaginary part of the complex input value is always 0 (and yet in the output it is not).
- In the case of either real or complex FFTs, what does the imaginary number represent both before and after running the FFT?
- Does the imaginary number play a role in calculating the phase offset?
- What information is lost (if any) by entering input values with 0 as the imaginary component?