Most speech scrambling systems are either linear periodic filters or can be modeled as such. It is well-known that from an input-output point of view, a periodic filter is equivalent to a multi-input multi-output linear time-invariant system and thus a rational transfer matrix. In this paper, we propose a framework, based on transfer matrices and frequency domain descriptions, for analysis and design of speech scrambling filters. We derive necessary and sufficient conditions for a scrambling system to be insensitive to frame synchronization error. We propose a procedure for the design of scrambling filters that are insensitive to synchronization error and have zero bandwidth expansion. An illustrative design example is given.
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