Statistical analysis of temporal coherence function and its application in howling detection

Temporal coherence function (TCF) is first defined to measure the correlation between a wave and its delayed version in optics. Now, TCF is a basic physical quantity, that has already been applied to numerous fields. To the best of our knowledge, statistical properties of TCF have not been well studied until now. After defining TCF, this paper gives a new insight into it by studying its statistical properties, where its probability density functions (p.d.f.s) for different types of signals are given. Finally, TCF is applied to detect howling frequency, where we show how to choose the delay time in a best way for practical considerations. There are two benefits by using TCF in howling detection. First, its computation is extremely low. Second, the detection threshold can be easily chosen since TCF is a normalized measurement. Experimental results show the validity of TCF in detecting howling frequency.