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The modern day digital multi-channel FFT spectrum analyzer is proving to be an extremely useful tool for measuring the dynamic characteristics of electro-mechanical servo systems. Most of the commercially available analyzers can make Frequency Response Function (FRF) measurements very conveniently and accurately. Since this measurement data is in digital form it can be transferred from the analyzer to a computer and further processed to identify the characteristics of the servo-loop. This paper discusses a new approach for treating FRFs from a experimental and analytical point of view. A block of measurement data can be "curve fit" to identify the characteristic polynomial, or the poles, zeros, and residues of some portion of a servo-system. A new Rational Fraction Polynomial estimation algorithm has been developed by the authors for curve fitting these measurements, and its use is illustrated. Alternatively, other portions of a servo-loop can be represented analytically by their poles and zeros which can then be used to synthesize FRFs between any two points in the loop. Overall system stability can also be conveniently studied via the curve fitting process by determining the location of system poles as functions of controller parameters.