A Digital Interpretation of Frequency-Periodic Signal-Interference Microwave Passive Filters

This paper addresses, for the first time, the digital representation of spectrally periodic signal-interference microwave passive filters. Starting from the theoretical rational transfer function of a synthesized transmission-line signal-interference analog filter, the real-valued coefficients of its digital-domain filter counterpart are derived. This discrete-time formulation for this type of microwave filters allows to clarify some confusing concepts into them, such as filter order. Moreover, some particular phenomena observed in associated experimental proof-of-concept planar prototypes, such as the appearance of out-of-band/spurious resonance peaks, are also explained by this study as zero-pole quasi-cancellations. In addition, it is demonstrated here that the use of the adjective "transversal" for this class of microwave passive filters could be no rigorous as it is understood in a digital sense since its discrete-time modeling commonly obeys an infinite-impulse-response structure. For validation, the expounded theoretical framework is applied to three examples of signal-interference passive filters exhibiting quasi-elliptic-type single-passband, six-passband, and low-pass responses.