Matched-filter Theory for Doppler-Invariant Pulse Compression

From the relativistic constraints upon the reflection of electromagnetic waves from targets moving with constant velocities, the frequency-domain representation of the Doppler-invariant frequencymodulated signal is derived. This frequency spectrum of the signal uniquely defines the matched-pulse compression filter which approximates to a rectangular amplitude response with a hyperbolic group-delay characteristic over the passband. A maximally flat solution to the problem is derived in closed form and leads to explicit formulas for element values in the canonic nonreciprocal realization, thus enabling a large degree filter to be constructed without recourse to numerical synthesis.