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Instantaneous frequency (IF) estimation through the estimation of peak locations in the time-frequency plane is an important approach for signals contaminated with additive white Gaussian noise. In this paper, the forementioned analysis is carried out for continuous wavelet transform. The analysis of the scalogram as the instantaneous frequency estimator is performed for any FM signal regardless of the mother wavelet. Accurate expressions for the bias and the variance of the estimator are derived, and reveal that the bias and the variance are signal dependent. Results are statistically confirmed through the numerical analysis for several mother wavelets, and among considered wavelets, the Morlet wavelet produces the smallest estimation error. Furthermore, the performance of the IF estimator based on the scalogram and the spectrogram were compared through analysis of mean square error. These results showed that the scalogram with the Morlet wavelet exhibited good performance for the sample linear FM signal and the sample hyperbolic FM signal in comparison to the spectrogram.