Abstract： In the application of the non-sinusoidal orthogonal modulation system based on PSWF (prolate spheroidal wave function) in time domain it is difficult to generate PSWF in real-time and complex to realize the non-sinusoidal orthogonal modulation system. Therefore, starting from the Fourier series expansion of PSWF, the relationships between the expansion coefficients and the energy and orthogonality of PSWFs were analyzed. Then, a modulation method based on the inverse discrete Fourier transform (IDFT) and a demodulation method based on the discrete Fourier transform (DFT) were deduced. After that, structures of the modulator and demodulator based on the (inverse) fast Fourier transform (FFT & IFFT) were given. As the idea of Fourier transform was introduced to the realization of non-sinusoidal communication system, the connection between nonsinusoidal communication system and (inverse) discrete Fourier transform was established. This method may provide reference for the study of nonsinusoidal technology.