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A method is described for generating a precisely phase-controlled linear FM pulse of large time-bandwidth product T⋅W=N by digitally phase-modulating a square-wave carrier at frequency fo with phase jumps of magnitude π/m, where design parameters N and m are powers of 2. A parabolic function generator, which sequentially computes the square of the number of clock input pulses, furnishes modulation orders and is basically comprised of 2s+1 flip-flops (where 2s=m⋅N). Frequency of input pulses is m⋅W, where sweep bandwidth W has to be chosen smaller than 2fo/1+m. Phase quantization noise takes the place of “linearity” and “stability” concepts in analog linear FM generators, and its power can be controlled by design parameter m, with a reduction of 6 dB for each doubling of the value of m. Bandpass-filtering of the output-modulated signal gives, in many cases, a satisfactory signal-to-quantization noise ratio, even with m=2. [The system described was developed by the author and H. W. K. Kelly, now of Admiralty Research Laboratory, Teddington, England.]

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