An even time-domain function yields a purely real Fourier transform.

Evidence

Note, that in this case, F(ω) turns out to be real, that is, it has no imaginary part. This is a consequence of our defining f(t) as an even function. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2783

Categorization

• DEFINE: Symmetry in time produces zero imaginary part in frequency — a recurring shortcut in transform work.