A radar system uses LFM waveforms. The received signal is of the form \(s_{r}(t)=A s(t-\tau)+n(t)\), where \(\tau\) is a time delay that depends on range, \(s(t)=\operatorname{Rect}\left(t / \tau^{\prime}ight) \cos\) \(\left(2 \pi f_{0} t-\phi(t)ight)\), and \(\phi(t)=-\pi B t^{2} / \tau^{\prime}\). Assume that the radar bandwidth is \(B=5 \mathrm{MHz}\), and the pulse width is \(\tau^{\prime}=5 \mu\) s. (a) Give the quadrature components of the matched filter response that is matched to \(s(t)\). (b) Write an expression for the output of the matched filter. (c) Compute the increase in SNR produced by the matched filter.