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Discontinuities in stimulus.

Dear List,
I have a rather simple question concerning the usual assumption made about the need for "continuity" of a stimulus. My interest arose when I started exploring the "fluttering" sound heard for some stimuli. A simple way to create a stimulus to study this phenomenon was to insert periodic "discontinuities" in a pure sinusoid of low frequency by simply deleting bits from this stimulus in a consistent manner. My next step was to try and create a model, which became problematic as the resultant sound heard was dependent both on the size of the deleted section and also on where the deletion was performed. Does anyone have an easy method for determining first, that a discontinuity in the stimulus has occurred and second and more importantly, where.
Thanks in advance for any insights,
Randy Randhawa