Radar Signal !free! ⚡

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

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

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)). Disadvantage: More sensitive to Doppler shifts

Advantage: Lower range sidelobes than LFM (Barker codes give peak sidelobe 1/N). Disadvantage: More sensitive to Doppler shifts. A train of narrowband pulses at different carrier frequencies synthesizes wide total bandwidth. Enables high range resolution with lower instantaneous bandwidth hardware. 5. The Ambiguity Function The ambiguity function (\chi(\tau, f_d)) is the 2D autocorrelation of the radar signal, showing the response to a target at range delay (\tau) and Doppler shift (f_d): radar signal

[ s(t) = A \cdot \textrect\left(\fract\tau\right) \cos(2\pi f_0 t) ]