Abstract
This paper describes a method of estimating the gains at sample frequencies and the ℓ2 gain for a linear time-invariant discrete-time system using a truncated step response. The gain is estimated using a bandpass filter at each sample frequency, and the filter parameter is optimized by maximizing the estimate of the ℓ2 gain near the peak gain. This filtering method is extended to multivariable systems. Another method of making an optimal bandpass filter is derived from the iterative-experiment method. The filtering method is compared with other estimation methods in terms of noise sensitivity through a series of numerical experiments.
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