New Coherence Function with Measurements of One Sampling Period

The conventional coherence function has been widely used to evaluate qualities of frequency response functions (FRFs). It requires response and excitation series of at least two sampling periods to yield meaningful function values. In addition, errors in a FRF and its associated IRF that are caused by system errors, such as response advancement error between measured response and excitation series in a data acquisition system, can never be reflected in the conventional coherence function. A new coherence function is introduced to efficiently and physically evaluate qualities of FRFs, which can yield meaningful and stable values even when response and excitation series of only one sampling period are available, and it can reflect response advancement error between measured response and excitation series.