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Some radar systems employing a linear FM pulse require FM linearity not easily obtainable from present generation methods. A technique is developed whereby average linearities of better than 0.1 per cent may be realized by active generation methods. Two methods of implementation are described that synthesize the waveform by generating a staircase-type stepped FM waveform and "filling in" the steps with a suitable sawtooth FM signal. Coherence, required number of steps, Doppler, and random phase errors are considered.