What is a matched filter and why is it optimal for signal detection?

A matched filter maximizes output SNR at sampling instant for a known signal in additive white Gaussian noise. Its impulse response is time-reversed and delayed version of expected signal. For rectangular pulse s(t), matched filter is integrator sampled at pulse end. Mathematically, it correlates received signal with expected waveform. The matched filter is optimal because it concentrates signal energy at sampling instant while spreading noise. Used in radar, digital communications, and pattern detection. Implementation: FIR filter matched to pulse shape.