Complex gain

In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal. The term complex is used because mathematically this effect can be expressed as a complex number. In electronics, complex gain is the effect that circuitry has on the amplitude and phase of a sine wave signal. The term complex is used because mathematically this effect can be expressed as a complex number. Considering the general LTI system where f ( t ) {displaystyle f(t)} is the input and P ( D ) , Q ( D ) {displaystyle P(D),Q(D)} are given polynomial operators, while assuming that P ( s ) ≠ 0 {displaystyle P(s) eq 0} .In case that f ( r ) = F 0 cos ⁡ ( ω t ) {displaystyle f(r)=F_{0}cos(omega t)} , a particular solution to given equation is