In this paper, the designs of fractional delay filter, Nyquist filter, lowpass filter and diamond-shaped filter are presented. First, the relation between Nyquist filter and fractional delay filter is investigated such that the design tools of one filter can be applied to design the other filter. The conventional Lagrange FIR filter, Thiran allpass filter and Farrow structure are used to design Nyquist filter. Moreover, we also show how to design fractional delay filter by using the polyphase decomposition of Nyquist filter. Then, the relation between lowpass filter and lowpass fractional delay filter is studied such that the design methods of one filter can be utilized to design the other filter. Next, the relation between diamond-shaped filter and fractional delay filter is established such that the diamond-shaped filter can be designed by using fractional delay filter directly. Finally, several numerical examples are illustrated to demonstrate the effectiveness of the proposed design methods.