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Classic windows have constant time delay and linear phase because of the symmetry and the time shift causality-imposed in the time domain. And thus, all such windows have the same spectral phase response. Removal of the symmetry constraint on a classic window can result in a variable phase response and in an alterable time delay. In essence the time delay becomes shorter will bring about a lot of benefits in speech coding. Some asymmetric windows with better magnitude response also can lead to a better recognition performance if the result is relatively insensitive to phase distortion. However, it is surprising that so little attention has been paid to the asymmetric windows in past literature; and never in past history has this issue been systematically or comprehensively studied. As a result, several methods to obtain the asymmetric windows are being presented in this paper. The asymmetric windows are displayed and compared with the classic windows, concerning both in time and frequency domains. Some new asymmetric windows with good behavior are introduced. The work in this paper makes it possible for researchers to select an asymmetric window to meet their requirements, in terms of bias due to time delay or bias due to spectral behavior. Finally, the application in a new aspect, of the asymmetric windows, is displayed. The simulation demonstrates that the improved estimation method, in which the symmetric windows are replaced by the asymmetric windows, shows a stronger capability of additive noise resistance than the traditional method.

Asymmetric Windows and Their Application in Frequency Estimation