Improved Method for Frequency Estimation of Sampled Sinusoidal Signals Without Iteration

This paper presents a method for estimating the signal frequency of sampled sinusoidal signals, which does not require any iteration for the frequency search. A noniterative method of frequency estimation was already developed by Zhang , where an analytical expression for the signal frequency is obtained using the differences between the neighboring input data. However, this method is very susceptible to additive noise. This paper extends the algorithm of Zhang to maintain the same signal-to-noise ratio as with the traditional four-parameter estimation method that requires iterations for the signal frequency search. Unfortunately, the proposed method is unable to estimate the accurate frequency in the case of an infinite number of data points when noises are added to the signal. From a noise analysis, it was found that the average frequency estimation error becomes zero when using a (2/3)π phase interval to calculate the signal difference. Numerical simulation results show that the frequency estimation error when Gaussian noise is added to the input data is about 13% higher than the square root of the Cramer-Rao bound. An additional 6% error is also added when the phase interval for frequency estimation deviates 10% from (2/3)π . Furthermore, it was found that the effect of harmonic components on the frequency estimation error can be minimized when the phase interval is close to (2/3)π, and the total number of data sample covers several signal periods or truncated close to an integer multiple of the signal period. As a result, the frequency estimation with the proposed method is more than 40 times more accurate than that with the IEEE-1057 method when the harmonic components are added to the input signal, which is confirmed by numerical simulations.