Frequency Truncated Discrete-Time System Norm

Computation of the frequency truncated norm of a discrete-time linear time-invariant system is required in multi-rate digital signal processing and model reduction applications. For a system represented using state-space equations, the frequency truncated norm itself is a particular case of an integral of the transfer function of a discrete-time linear time-invariant descriptor system over a limited frequency band. This letter provides closed-form expressions for this integral and the frequency truncated norm for direct computation in terms of the principal logarithm and matrix exponential function.