Approximation of First–Order Complex Resonators in the Frequency–Domain

A novel approach for implementing first-order complex filters without the requirement of two separate signal paths, for the real and imaginary parts of the transfer function, is introduced in this work. This is achieved by employing a curve-fitting based method to approximate both the gain and phase responses of the prototype complex filter. The resulting rational integer-order transfer function can be realized using conventional filter design techniques. The behavior of the proposed complex resonator configuration is evaluated through experimental results, derived using a Field Programmable Analog Array (FPAA) device. An application example is provided, in which the complex resonator is employed to extract vowels from the corresponding glottal pulse trains.