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The usefulness of the periodogram as a system identification tool is often underestimated because of the large variance in the estimates of the power spectral density function of the system output. If we approach the parameter estimation problem as an exercise in maximum likelihood estimation, with the measured periodogram as the input data, the result is a spectral matching technique that is rather simple to apply. A valuable by-product of this method is a value for the Fisher information matrix of the parameter estimates. Models of many forms such as AR, ARMA, with or without observation noise can be treated using the same algorithmic structure. The input data can be efficiently computed using the Fast Fourier Transform. Several examples illustrate the technique.