A digital signal demultiplexing apparatus that can demultiplex and a digital signal multiplexing apparatus that can multiplex signals of channels having arbitrary frequency intervals and bandwidths are provided. The digital signal demultiplexing apparatus performs discrete Fourier transform on an input signal, output samples existing within frequency bands of each channel from samples of the frequency domain, add samples such that the number of samples of each channel become a power of two, and performs, on the samples of each channel, discrete inverse Fourier transform of a length the same as the number of the samples. The digital signal multiplexing apparatus performs discrete Fourier transform of a length the same as the number of samples of an input signal for a predetermined period, outputs samples existing within frequency bands of each channel from samples of the frequency domain of each channel, and arrange the samples according to frequency assignment of each channel to perform discrete inverse Fourier transform.