Signal Definition

First, we will choose a signal convenient for the test: $y(t) = e^{j \alpha t^2}$ where $\alpha$ is a constant indicating the slope of the frequency change. We can think of the signal as going from infinitely negative frequency at negative infinite time to positive infinite frequency at positive infinite time. In any case, the signal's frequency is 0 (DC) at time 0; this signal has even symmetry with respect to time, that is: $y(t) = y(-t)$ Thus we know that for $Y(\omega) = \mathcal{F}\{y(t)\}$ $Y(\omega) = Y(-\omega)$.