The spin modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes tumbling and inspiralling into massive black holes have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this article we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just three or four, much smaller than what has hitherto been thought to be about nine or ten. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte-Carlo simulations to test the predictions made in this paper.
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