A Frequency discriminator based on a combination of Discrete Fourier Transform (DFT) operator and half-bin DFT operator, corresponding to a set of Twiddle factors with frequency double than the sampling frequency. The frequency estimators are so chosen as not to have any zero or discontinuity point. Therefore the discriminator of embodiments of invention is more stable and well-behaved in an extended operating range. The discriminator of the invention, when applied to a Global Positioning System (GPS) receiver, allows a safer lock to the carrier frequency, even in presence of a large initial error, and avoids the problem of false locks.