Development of high-performance signal processing systems by analytical synthesis of high-accuracy digital filter structures

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We have derived a general expression of the transfer function of digital filters with all second-order modes equal. For the case of second-order digital filters, the transfer functions can be expressed in closed form. Furthermore, we show that the general expression is obtained by a frequency transformation on a first-order prototype FIR digital filter. Furthermore, we have numerically shown the absence of limit cycles of the minimumL_2-sensitivity realizations subject to L_2-scaling constraints of second-order digital filters.