The convergence properties of the Carson and Fry and of the van der Pol-Stumpers expansions for the complex amplitude of the steady-state response of a filter to an FM excitation are discussed. The theory of quasi-stationary analysis and of FM-to-AM conversion with low distortion is presented. The use of Taylor's formula leads to error estimates and to a simple condition that specifies an upper bound on the error incurred in restricting the solution to the quasi-stationary term (the instantaneous-frequency method). A sluggishnes atio and an index of stiffness are defined for filters whose system functions have poles only in the, left, half-plane. Sluggishness ratios and indices are given for various filters of wide practical interest.
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