Synthesis of linear-phase selective filters based on maximum of time-domain response

Popular selective filters are obtained by the approximation of the rectangular magnitude response. Similarly, popular delay filters are obtained by the approximation of the linear phase. The design of these filters is performed in the frequency domain, ensuring optimum behavior in the maximally flat, minimax, or least-squares sense. In this paper, we present a class of linear-phase selective filters which is obtained using time-domain synthesis. The filters obtained have impulse responses that approximate the impulse response of the ideal lowpass filter in the least-squares sense. It is shown that such an approximation can be obtained by maximization of the peak amplitude of filter´s response to the zero-phase sinc pulse. The features of the obtained filter class are presented and the transfer function parameters are provided.