FIR digital filter redesign via sampled-data <i> H _∞ </i> discretization in low-frequency domain

In this paper, a finite impulse response (FIR) digital filter is redesigned to approximate a delayed analog one via sampled-data <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> discretization in low-frequency domain. First, based on a continuous-time lifting technique, an infinite-dimensional error system is obtained by comparing the delayed analog filter with the FIR digital filter accompanied by an ideal sampler in front and a zero-order holder behind. Then, a finite-dimensional error system, which is satisfied with an equivalent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> norm with infinite dimensional in low-frequency domain, is acquired by a fast sampling/holding approximation and a discrete-time lifting technique. Furthermore, the FIR digital filter is attained with stability and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> performance for the finite-dimensional error system in low-frequency domain. Finally, a numerical example is presented to show the validity and superiority of the FIR digital filter redesign.