Resonator Fourier transform
Yukihiro Tadokoro, K. Noguchi · 2003
This paper proposes a new discrete Fourier transform algorithm using resonator H(z) = 1/(1 + z/sup -2 /). We call this algorithm the resonator Fourier transform (RFT). In the RFT, to calculate Fourier coefficients a/sub k/ and b/sub k/ of a frequency component f/sub k/, we sample an input signal x(t) by a sampling frequency f/sub s/ = 4f/sub 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/sub k/ or b/sub 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.