A method and apparatus for estimating the frequency of a dominant periodic component in an input signal by modelling the input signal using auto-regressive models of several different orders to generate candidate frequencies for the periodic component, generating synthetic sinusoidal signals of each of the candidate frequencies, and calculating the cross-correlation of the synthetic signals with the original signal. The frequency of whichever of the synthetic signals has the highest cross-correlation with the original signal is taken as the estimate of the frequency for the dominant periodic component of the input signal. The method may be applied to any noisy signal which has a suspected periodic component, for example physiological signals such as photoplethysmogram signals, and in the estimation of heart rate and breathing rate from such physiological signals.