New FIR Filter Design for Both Spectrum Matching and Inverse System Approximation

In this paper, a new design approach is presented for the transmitter filters which can match the desired or available spectra in a cognitive communication system. Since the corresponding receiver (recovery) filters are necessary to be considered, our proposed design scheme also imposes the constraints on the approximation errors associated with the receiver filters. A new measure is proposed here to quantify the difference between the desired spectrum and the actual spectrum resulting from the transmitter filter based on the Possion-Jesen formula. Moreover, different from many existing works for designing spectrum-shaping filters, our scheme also considers the inverse system at the receiver (receiver filter) jointly to recover the distorted signals caused by the transmitter filter. The approximation error of the inverse filter is measured by our recently derived L₂ error function. Our proposed filter design scheme for telecommunication transceivers should be able to provide novel spectrum-shaping solutions to the future cognitive radio technology.