Definition of a Linear Frequency Chirp Function and its FFT

We begin by considering the windowed discrete time function

$$y(n) = w(n) e^{i \alpha n^2}$$ (14)

where $w(n)$ is an $N-$sample ($N$ odd) discrete time windowing function valued from $-(N-1)/2$ to $(N-1)/2$ and $\alpha$ is a positive constant equal to half the linear frequency increase per sample in radians. As noted earlier, we will consider the decreasing frequency chirp case in section 3.6.