Time-domain synthesis of linear-phase selective filters

Time-domain synthesis is used when a system is required that gives a prescribed response for a given excitation. It is typically used in the design of systems that approximate the particular impulse response or particular step response shape. Furthermore, it is used in the design of systems that introduce small time-domain distortion. It is less known that the time-domain synthesis can also be used to obtain frequency-selective systems. This paper describes the time-domain synthesis of continuous-time linear-phase selective filters. The design is based on numerical optimization. Starting from the impulse response of an ideal lowpass filter, the optimization problem is formed. The optimum is found using a general-purpose method for nonlinear optimization. The parameterization of the transfer function being optimized is considered to accomplish the best control of filter´s complexity. The design procedure is described and two examples are worked out.