Nyquist filters for pulse shaping and related matched filters in wireless communications are disclosed that provide improved performance. The disclosed embodiments recognize that the second derivative of the raised cosine function is discontinuous in the frequency domain and that the first derivative of the square root raised cosine is discontinuous in the frequency domain. As such, a generalization for the raised cosine filter is applied, and improvements can be made to the raised cosine function time-frequency localization and ultimately to tradeoffs between inter-symbol interference and adjacent channel interference by introducing smoothness to the higher order derivatives of the frequency response.