Radar Signal 【99% TRUSTED】

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

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

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)). The matched filter output for a signal (s(t))

After matched filtering, the output envelope is a function with first nulls at (\pm 1/B). LFM is Doppler-tolerant (slight frequency shifts cause small range shifts but minimal SNR loss). 4.2 Phase-Coded Signals The pulse is divided into sub-pulses (chips), each with 0° or 180° phase according to a binary sequence (e.g., Barker code, Gold code). Bandwidth (B \approx 1/t_chip), time-bandwidth product equals the number of chips. Gold code). Bandwidth (B \approx 1/t_chip)

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