I am computing the zero delay cut of the ambiguity function a LFM chirp: $\chi(\tau = 0, \nu) = \int_{-\infty}^{\infty} u(t) u^{*}(t)e^{j 2 \pi \nu t} dt = \int_{-\infty}^{\infty} A e^{j(2 \pi f_0 t + 2 \pi \frac{k}{2} t^2 + \phi_I)} A e^{-j(2 \pi f_0 t + 2 \pi \frac{k}{2} t^2 + \phi_I)} e^{j 2 \pi \nu t} dt = \int_{-\infty}^{\infty} A^2 e^{j 2 \pi \nu t} dt$

I have to compute the module, or the absolute value, of $\chi(\tau = 0, \nu)$ to obtain my value. This is, I am searching for:

$\left|\int_{-\infty}^{\infty} A^2 e^{j 2 \pi \nu t} dt\right|$

I know, because I have computed it with Matlab, that the value should be around 13.2 dB. Can anyone resolve the integral?


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