To provide a filter device that has a simple configuration, changes a stop band instantaneously, reduces noise efficiently, and can perform filtering speedily and precisely, and to provide a method of designing a digital filter.

In the filter device whose stop band is variable, and the method for designing the digital filter, the coefficients of the digital filter are obtained by formulating to a least square approximation problem or a half positive definite value schedule problem so that at least one of a plurality of stop bands in the digital filter having a plurality of stop bands according to the coefficient coincides with a desired frequency.