Resonator Fourier transform

This paper proposes a new discrete Fourier transform algorithm using resonator H(z) = 1/(1 + z^-2 ). We call this algorithm the resonator Fourier transform (RFT). In the RFT, to calculate Fourier coefficients a_k and b_k of a frequency component f_k, we sample an input signal x(t) by a sampling frequency f_s = 4f_k and accumulate the sampled values x(n) by a resonator, that is, y(n) = x(n) - y(n - 2), and then divide the accumulated value y(n) by the sample number. By these processing, we can obtain a_k or b_k using some subtractions and only one multiplication for a mean operation. We consider the orthogonality of the RFT and compare the features of the RFT with the conventional DFT.