This paper presents a new method for estimating rate of change of frequency (RoCoF) of voltage or current signals measured using instrument transformers. The method is demonstrably superior to currently available methods in literature, in terms of estimation-latency and estimation-error. The estimation is performed in two steps. In the first step, the analog voltage or current signal obtained from an instrument transformer is statistically processed using interpolated discrete Fourier transform in order to obtain the means and variances of the signal parameters. These means and variances are then given as inputs to the second step, in which Kalman filtering is used to find the final RoCoF estimate. Accurate mathematical expressions for the means and variances of signal parameters have been derived and used in the second step, which is the main reason behind the superior performance of the method. The applicability of the method has been demonstrated on a benchmark power system model.