This lecture covers the synthesis of specific filters, including analog filters, linear phase filters, and rational transfer functions. It discusses the frequency response, step response, and impulse response of analog filters, as well as the classification of analog filters based on causality and phase distortion. Compromises in filter design, frequency specifications, and group propagation time are also explored. The lecture delves into the concept of linear phase filters, their impulse response, and the effects of even and odd symmetry. Additionally, it explains the calculation of impulse response for linear phase filters and the frequency response of real, pure linear phase low-pass filters.