Repeated convolutions of Butterworth-filtered spectra
A.A. Ali · IEEE Transactions on Circuits and Systems · 1984
For a low-passn-pole Butterworth filtered spectrum, repeated convolutions are derived in a closed form. Repeated convolution of ordermresults when a signal is convolved with itselfmtimes. The derivation is based on the "convolution-multiplication" property of the Fourier transform. The results are useful in determining the FM spectra of Butterworth filtered Gaussian processes.