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This paper develops a systematic approach to select a timedependent state transformation which can map a linear time-variant (LTV) digital filter to an equivalent filter having diagonal state-feedback matrices. Due to the structural simplicity of the diagonal systems, this time-dependent state transformation is a convenient tool for analyzing recursive LTV filters expressible in the state-variable form. In this paper, we discuss both the theoretical basis and the application of this diagonalization procedure. The properties of two types of recursive LTV filters are examined by using this state transformation technique. Based upon the separable properties of the impulse responses, we have explored a new algorithm for synthesizing desired impulse responses with a major class of recursive LTV filters. This technique, though suboptimal, can substantially reduce the computation required in the synthesis procedure.