Not really a homework question, but related none the less. I'm confused about what exactly the amplitude spectrum is. As well as the power spectrum.
Not really taking a purely mathematical approach here, I'm using numpy for python. Specifically the fft module to produce:
f(t) = sum of 3 waves; same amp, phase; varying angular frequencies e.g. 3, 8, 5
F(freq) = fft(f): Fourier transform of f
freq = fftfreq(len(f)) dt): Produces frequency bins for F
amp_spec = abs(F)
pow_spec = amp_spec**2
The Attempt at a Solution
From what I gather, it is the absolute value of the Fourier Transform which is somewhat like a histogram of frequencies of the components that the initial f(t) wave oscillates at.
When I plot the graph amp_spec vs. freq, I get something similar to what I expect --peaks at 3, 8 and 5. But there is a mirror of this graph on the negative x axis which I do not know the reason for but I suspect is just the way the function calculates the values (please correct me if I'm wrong).
The major question for me is what exactly does the value for the amplitude spectrum represent? When I use a dt (for my time array) of 0.01, I get the first graph shown below with ~250 as the max value on the y axis. But when I use 0.001 as my dt, the max value on the y axis shoots up to ~2500. Incidentally, the number of frequency bins also goes up for reasons I also don't know...
Another question I have is what units would the y axis be in? That and once I figure out what the amplitude spectrum is, what would the power spectrum be?
I've tried google with varying key terms and I still can't get a definite answer.