document: Efficient tracking of the cross-correlation coefficient In many -LRB- audio -RRB- processing algorithms , involving manipulation of discrete-time signals , the performance can vary strongly over the repertoire that is used . This may be the case when the signals from the various channels are allowed to be strongly positively or negatively correlated . We propose and analyze a general formula for tracking the -LRB- time-dependent -RRB- correlation between two signals . Some special cases of this formula lead to classical results known from the literature , others are new . This formula is recursive in nature , and uses only the instantaneous values of the two signals , in a low-cost and low-complexity manner ; in particular , there is no need to take square roots or to carry out divisions . Furthermore , this formula can be modified with respect to the occurrence of the two signals so as to further decrease the complexity , and increase ease of implementation . The latter modification comes at the expense that not the actual correlation is tracked , but , rather , a somewhat deformed version of it . To overcome this problem , we propose , for a number of instances of the tracking formula , a simple warping operation on the deformed correlation . Now we obtain , at least for sinusoidal signals , the correct value of the correlation coefficient . Special attention is paid to the convergence behavior of the algorithm for stationary signals and the dynamic behavior if there is a transition to another stationary state ; the latter is considered to be important to study the tracking abilities to nonstationary signals . We illustrate tracking algorithm by using it for stereo music fragments , obtained from a number of digital audio recordings
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extractive_keyphrases: efficient tracking warping operation deformed correlation sinusoidal signals convergence behavior stationary signals dynamic behavior stationary state nonstationary signals tracking algorithm stereo music fragments
abstractive_keyphrases: cross-correlation coefficient audio processing algorithms discrete-time signals time-dependent correlation recursive formula digital audio recording