A matched filter is the optimal linear filter for maximizing signal-to-noise ratio in white noise: h(t) = s*(T-t), the time-reversed conjugate of the transmitted signal. The output is the cross-correlation of the received signal with the template, peaking at the signal delay. By the Schwarz inequality, this achieves the theoretical maximum SNR = 2E/Nā, where E is signal energy. In radar, pulse compression uses chirp (LFM) signals ā the matched filter output (sinc-like peak) has time-bandwidth product TW ā« 1, simultaneously achieving high energy and fine range resolution.