Nyquist filters play a very important role in data transmission to band-limit data spectrum and minimize intersymbol interference. Many different approaches to design such filters have been discussed in publications. Farhang-Boroujeny introduced a method to minimize a cost function using iterative least-squares method. The design can strike a balance between the stopband attenuation, the residual intersymbol interference (ISI), robust sensitivity to timing jitter and reduced peak-to-average-power ratio (PAPR). In this thesis, a novel method is proposed to achieve above properties by adopting Chebyshev minimax method to minimize the modified cost function. Compared the results obtained from the least-squares method and root raised cosine (RRC), for some filter specifications, the proposed designed filter outperforms the least-squares method and RRC.