Weighting Effect on the Discrete Time Fourier Transform of Noisy Signals

Weighting functions are usually applied to signal samples in order to reduce spectral leakage. This paper investigates the effect of weighting on the uncertainty of the Discrete Time Fourier Transform (DTFT) samples of a signal corrupted by additive noise. Making very weak assumptions, it is shown how the adopted window sequence and the autocovariance function of the noise affect the second-order stochastic moments of the frequency-domain data. The relationship obtained extends the results reported in the literature and is useful in many frequency-domain estimation problems. As an example of its application it is shown how the knowledge of the second-order moments of the transform has allowed the application of the least squares technique for the estimation of the parameters of a multifrequency signal in the frequency-domain. The estimator obtained has shown to be very useful when high-accuracy results are required under real-time constraints. The proposed procedure is shown to exhibit a better accuracy than other similar frequency-domain methods proposed in the literature. © 1991 IEEE