This paper treats the design of periodical notch filters with a given fundamental frequency and a given notch bandwidth. The method used in this work is based on the design of an allpass filter. The allpass filter is designed by solving a linear system of equations. This procedure reduces the complexity of the design while guarantees the precision on the rejected frequencies. It is also presented a method to improve the notch bandwidth characteristics of the periodical notch filter. Finally, it is shown that the resulting filter has a good behaviour when quantization is applied, if an adequate structure is used for the implementation.