1. A digital filter device, comprising: at least one hardware processor configured to implement: a fast Fourier transform device, the fast Fourier transform device comprising a first transform unit and a first data sorting processing unit the first transform unit performing one of a fast Fourier transform and an inverse fast Fourier transform, generating a plurality of first output data, and outputting the plurality of first output data in a first order, and the first data sorting processing unit rearranging the plurality of the first output data outputted in the first order, in a second order based on an output order setting; a complex conjugate generation unit generating second complex data, the second complex data including respective conjugate complex numbers of complex numbers, all of which composing a plurality of frequency-domain first complex data generated by Fourier-transforming a plurality of first input data of inputted time-domain complex numbers by the fast Fourier transform device; a filter coefficient generation unit generating a first and a second frequency-domain filter coefficients of complex numbers from a first, a second, and a third input filter coefficients of inputted complex numbers; a first filter unit performing a filtering process on the first complex data with the first frequency-domain filter coefficient and outputting third complex data; a second filter unit performing a filtering process on the second complex data with the second frequency-domain filter coefficient and outputting fourth complex data; and a complex conjugate synthesis unit generating fifth complex data by synthesizing the third complex signal and the fourth complex signal.