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This paper is concerned with techniques for the determination of all the critical frequencies (i.e., all the poles and zeros) of the transfer function of a linear time-invariant singleinput single-output system. Unlike methods involving the computation of polynomial coefficients, the techniques presented find the transfer zeros as the eigenvalues of a matrix obtained from the state and output equations of the system. A computational assessment is given with illustrative examples. In particular, the computation of actual bounds on the critical frequencies is discussed, and the application of these techniques to frequency analysis of networks is considered. Preliminary computer test results have confirmed that they require significantly less computation time and admit the possibility of detailed roundoff error analysis.