A new family of windows — convolution windows and their applications

A new family of windows is constructed by convolutions via a few rectangular windows with same time width and is thus referred to as convolution windows. The expressions of the second-order up to the eighth-order convolution windows in both the time and frequency domains are derived. Their applications in high accuracy harmonic analysis of periodic signals are investigated. Comparisons between the proposed windows and some known windows with the same width shows that, when the synchronous deviation of data sampling is slight, the proposed ones have the least effect of spectral leakage. Therefore, the new windows are well suited for high accuracy harmonic analysis and parameter estimation for periodic signals. The error analysis and computer simulations show that the estimation errors, corresponding to frequency, amplitude and phase of every harmonic component of a signal, are proportional to the pth power of the relative frequency deviation in case of the pth-order convolution window is applied to windowing signal of approximately p cycles. By introducing real time adjustment in sampling interval, the proposed algorithm can adaptively trace signal frequency and lead to less sampling synchronous deviation. The proposed approach has the advantages of easy implementation and high measure precision and can be used in harmonic analysis of quasi-periodic signals whose fundamental frequency drifts slowly with time.