A method to evaluate accuracy of FFT-based periodicity analysis for short length signal in low SNR

Described is a new method to evaluate theoretically and quantitatively the estimation error (bias error and variance) of the periodicity analysis when the fast Fourier transform (FFT) is applied to a sinusoidal signal in arbitrary signal-To-noise ratio (SNR) cases and when various windows are employed. The resultant quantitative evaluation of the estimation error is useful in many applications of various field to evaluate the bias error and uncertainty in the obtained spectrum. This method is also applied to design the optimum window function to minimize windowing defects, especially for short-length signals. Thus, the evaluation method proposed should play a significant role in the field of nonparametric spectrum estimation.