February Fourier Talks 2006

FM Perturbation due to near-identity Systems

The disturbance induced in the frequency modulation (FM) of an analytic signal due to its passage through a linear system is the main topic of this talk. For the case that the linear system is close to an identity system, a closed form approximation to the induced FM perturbation is derived. Taking the form of a linear operator acting on a system impulse response, the operator represents a well-behaved approximation to the true ill-behaved underlying non-linear operator. In its approximate linear form, the operator is amenable to standard linear theory. In addition, practical constraints including passband smoothness, zero group delay, and time-localization, are facilitated in the analysis. Applied in the context of RF system design, the FM perturbation analysis yields practical and useful performance bounds relating system parameters to induced FM deviation.