Radar Signal Link

[ |\chi(\tau, f_d)| = \left| \int_-\infty^\infty s(t) s^*(t+\tau) e^j2\pi f_d t dt \right| ]

The matched filter output for a signal (s(t)) in white noise maximizes the Signal-to-Noise Ratio (SNR) and is given by the convolution with the time-reversed complex conjugate: (h(t) = s^*(-t)). radar signal

The transmitted signal is (s(t) = \textrect(t/\tau) \cos(2\pi f_0 t + \pi \fracB\tau t^2)). radar signal

Resulting compressed pulse width: (\tau_comp = 1/B). Range resolution improves to (\Delta R = \fracc2B), independent of the original pulse width. 4.1 Linear Frequency Modulated (LFM) Chirp The instantaneous frequency changes linearly over time: (f(t) = f_0 + \fracB\taut). radar signal