Phase errors in the cross spectrum estimate due to misalignment

When the cross spectrum is estimated where there is a delay between the two input signals, it is shown that the corresponding misalignment gives both magnitude and phase errors. The existence of the phase error is a new result. The importance of the errors depend on the algorithms used. It is shown that the misalignment may either be given by the total observation time or by the section length in the processor. In the latter case the effect of phase errors must be considered when the section length is low, that is when the cross spectrum is smooth, requiring little resolution.