A periodically time varying digital filter containing an inverse discrete Fourier transformer and its application to the spectrum scrambling

An output sampling polyphase model containing an inverse discrete Fourier transformer is proposed and analyzed. The input-output relationship of the proposed model is obtained, and its periodically time varying property is discussed. An application of the proposed model to spectrum scrambling is considered. A structure suitable for realizing the spectrum scrambling within the scope of real computations is presented, and its design procedures based on the bifrequency map are described. It is demonstrated that the proposed structure can be used to implement a spectrum scrambler, whether FIR or IIR (finite or infinite impulse response) filters are used. A design example is given to verify the effectiveness of the proposed design procedures for the realization of a spectrum scrambling system when both FIR and IIR time-invariant filters can be used