FFT coefficients question

Question

I'm a software engineer working on DSP for the first time.

I'm successfully using an FFT library that produces frequency spectrums. I also understand how the FFT works in terms of its inputs and outputs, in particular the contents of the two output arrays:

Now, my problem is that I'm reading some new research reports that suggest that I extract: "the energy, variance, and sum of FFT coefficients".

1. What are the 'FFT coefficients'? Are those the values of the Real and Imaginary arrays shown above, which (from my understanding) correspond to the amplitudes of the constituent cosine and sine waves?

2. What is the 'energy' of the FFT coefficients? Is that terminology from statistics or from DSP?

Answer 1

1. You are correct. FFT coefficients are the signal values in the frequency domain.
2. "Energy" is the square modulus of the coefficients. The total energy (sum of square modulus of all values) in either time or frequency domain is the same (see Parseval's Theorem).