I'm a Biology Ph.D. student with some math literacy (multivariable calc, discrete math, linear algebra, quantum chemistry) under my belt, so apologies if my knowledge is substandard for the work I'm trying to do. I am currently looking at some time series of environmental data sampled every 20 minutes (temperature, etc). With help from a Geology professor, I am teaching myself some time-series analysis techniques and had some quick questions about the Fourier Transform.
My understanding: F.T. involves plotting your time series in the complex plane in polar coordinates, and averaging your points into a vector. Changing a multiplier (radians per timepoint) changes the vector, because… no correlation would cause the points to average out to zero, but any 'resonance' would cause the data to pull the vector off of 0.
The point where I'm having trouble, theoretically, is understanding what the imaginary component of the frequencies represents. I understand that in negative frequencies, imaginary components are odd and reals are even. I also understand that when you're looking at the One-sided power spectrum, you end up using the magnitude of the vector to determine power. This also makes sense to me.
Is having an imaginary component to the data just an incidental happenstance that results from utilizing the complex plane? Using this makes sense to me in that you're taking advantage of Euler's equations (which I'm sure helps with a lot of the math), but is there any sort of real-world meaning to imaginary components of frequencies?
Also, my conceptual understanding of Fourier comes from using my data, which does not have an imaginary component to it. How does plotting the data in the complex plane work when you start thinking about an input with both real and imaginary components?