Optimization-Free Filter and Matched-Filter Design through Spatial and Temporal Soft Switching of the Dielectric Constant

The problem of inverse design is rooted to the classical scattering. In general, these highly nonlinear and often ill-posed problems are solved via extensive optimization techniques. this paper, we suggest an optimization-free method for a one-dimensional medium with spatially inhomogeneous dielectric constant $?(z)$. addition, derive governing equation analog problem---a time-dependent homogeneous medium---and use same technique temporal profile $?(t)$ that required achieve desired frequency response in $k$-space. Lastly, inversion approach demonstrate reflection such reflected wave undergoes filtering, as Tchebychev type, differentiator, matched filter chirp signal detection over additive Gaussian noise, which high potential significance radar sonar applications.