I was hoping to clarify if the following was correct:
A real function (neither even nor odd) in time exhibits conjugate symmetry in frequency, so the real part of the frequency response is even, and the imaginary portion is odd
A real, even function has a frequency response that is strictly real and even
An imaginary, odd function has a frequency response that is strictly imaginary and odd
-also: Can anything be said if the function were imaginary in time (neither odd nor even)? Would it be anti-conjugate symmetric, so the frequency response would be such that the real part is odd and the imaginary portion is even?