Phase-Sensitive Dynamic Filters: A Conceptual Model for Energy-Preserving, Instantaneously Tunable, Symbol-Level Signal Processing Using Complex IIR Filters

Filters used for modulated RF signals are often matched bandpass filters that have larger bandwidths than that of the modulation. Therefore, the time constants of the filters must be shorter than the symbol periods. This paper presents an idealized theoretical model for Phase-Sensitive Dynamic Filters (PSDF), a class of emerging filters that can be tuned in real time, as fast as the symbol rate of a signal but with time constants longer than the symbol periods. With the foreknowledge of the frequency and phase shifts of a given signal, such filters are capable of filtering across multiple symbols of a constant envelope and compressing the noise bandwidth to a fraction of the modulated signal bandwidth. The transient response of the filters can be longer than the symbol rate of the signal. This can mathematically be modeled by infinite impulse response (IIR) filters with long time constants yet fast time-varying complex coefficients in the feedback path. Phase-sensitive dynamic filters preserve energy across symbols and also exhibit phase-sensitivity. The proposed models indicate that PSDFs can be employed in applications such as rejection of self-interference in the front ends of full-duplex communications systems. Such systems pave the way for the possibility of higher isolation and robustness compared to other prototypical approaches in dynamically changing systems.