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For good radar system performance, a transmitted waveform is desired that has 1) wide bandwidth for high range resolution and 2) long duration for high velocity resolution and high transmitted energy. In a pulse-compression system, a long pulse of duration T and bandwidth F (product of T and F greater than one) is transmitted. Received echoes are processed to obtain short pulses of duration 1/F. Compression ratio (the ratio of long-pulse duration to short-pulse duration) is thus the product TÂ·F, and is a measure of the combined range and velocity resolution. Pulse compression occurs if a waveform with a nonlinear phase spectrum is passed through a filter ``phase matched'' to the waveform. Phase matched means that the nonlinear part of the network phase response is the negative of the nonlinear part of the waveform phase spectrum. The waveform with rectangular amplitude spectrum and parabolic phase spectrum is ideally suited for pulse compression. Bandwidth and duration can be independently specified, duration-bandwidth products of 100 or more are presently feasible, and the waveform remains phase matched to one filter over a wide range of Doppler frequency shifts.