² This paper describes the model reduction framework for single-input single-output (SISO) discrete-time systems based on the preservation parameters such as Markov properties of the original system by applying a Frequency-Limited Impulse Response Gramian based Balanced Truncation method. This proposed method extends the Frequency-Limited Impulse Response Gramians model reduction method for continuous systems described in the recent paper in [20] to be applicable for discrete time systems. A

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... erical example is provided to compare the performances between various frequency limited model reduction methods at an arbitrarily selected frequency range within the passband of a digital filter. The stability of the reduced order models are also checked for each scenario.