A realization of real filters using complex resonators

Abstract

AbstractThe synthesis of real filters using the complex coefficient filters is considered interesting in digital signal processing, since one can expect that the freedom in the design will be increased and the coefficient sensitivity will be decreased. In analog signal processing, on the other hand, there are few reports on the design of the filter from a similar viewpoint.This paper discusses the complex coefficient filter on the analog domain, which is obtained by shifting the frequency response of the lower‐order real filter on the frequency axis, together with its application to synthesize real filters.First, the complex analog transfer function is introduced, which is obtained by shifting the frequency response of the real filter on the frequency axis. The elements for the complex analog signal processing are defined. Then, using those elements, the complex resonator is proposed.The proposed circuit can be considered as a special class of the biquad circuit, where the complex conjugate poles of the second‐order section are specified. As a result of sensitivity analysis, the proposed circuit is shown to have the same or lower sensitivity as that of the biquad circuit. Another feature is that the circuit can be realized using the lossy integrators and can be used as the functional unit in the active filter to be operated at higher frequencies. Design examples using the operational amplifier and their experimental results are shown to verify the effectiveness of the proposed method.