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This Fourier transform is given in tables [1, 21 only in the case when k = 1 and c = 2 cos e with -i < e < fr. The need for it in other cases has arisen in recent work concerned with the study of a random signal obtained by applying a white noise to the input of a band pass filter. The power transfer function of the filter, and thus the power spectrum of the signal at the filter output, is considered to be of the form

The Fourier transform of [𝑐^{2𝑘}+(𝑥-𝑥⁻¹)^{2𝑘}]⁻¹ arising from study of tuned circuit spectra