Closed Form Expressions of Balanced Realizations of Second-Order Analog Filters

Closed Form Solutions to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters with Real Poles

This letter proposes closed form solutions to the L2sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functi...

Closed-form Frequency Estimation Using Second-order Notch Filters

In this paper the problem of the frequency estimation of a sinusoid embedded in white noise is considered. The approach used herein is the minimization of the sample variance of the output of constrained notch filters fed by the noisy sinusoid. In particular, this paper focuses on closed-form expressions of the frequency estimate, which can be obtained using notch filters having an all-zeros FI...

Analytical synthesis of minimum L2-sensitivity realizations of all-pass digital filters

This paper proposes analytical synthesis of the minimum L2-sensitivity realizations of all-pass digital filters. We first prove that the L2-sensitivity minimization problem can be solved analytically if the all second-order modes of a digital filter are equal. We focus on the fact that the second-order modes of all-pass digital filters are all unity. As a result, it is clarified that the minimu...

Educational Article:Gramians and Balanced Realizations and their Application in System Order Reduction

Educational Article:Gramians and Balanced Realizations and their Application in System Order Reduction