Digital Generation of a Linear FM Pulse of Given Time‐Bandwidth Product

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 Admiralt...