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This paper gives a procedure for designing an FM signal of arbitrary envelope shape so that it will have a specified spectral modulus and hence, a specified autocorrelation function. The design procedure, which is based upon an approximate analysis, gives best results when the duration-bandwidth product of the signal is large, and it is therefore useful in the design of pulse compression signals. Examples are given to illustrate the design procedure and to show in a general way how the quality of the approximate solution depends upon the duration-bandwidth product of the signal and upon the shape of the signal envelope and the modulus of the signal spectrum.
Evert N. Fowle (1964) studied this question.