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Instantaneous frequency (IF) is a fundamental concept that can be found in many disciplines such as communications, speech, and music processing. In this letter, analysis of an IF estimator, based on a time-frequency technique known as S-transform, is performed. The performance analysis is carried out in a white Gaussian noise environment, and expressions for the bias and the variance of the estimator are determined. The results show that the bias and the variance are signal dependent. This has been statistically confirmed through numerical simulations of several signal classes.