It is well known that a function can be decomposed uniquely into the sum of an odd and an even function. This notion can be extended to the unique decomposition into the sum of four functions – two of which are even and two odd. These four functions are eigenvectors of the Fourier Transform with four different eigenvalues. That is, the Fourier transform of each of the four components is simply ...

The Fast Fourier Transform (FFT) is based on an important factorization of the Fourier matrix Fn into a product of sparse matrices. In this paper, we demonstrate the existence of a set of FFT-like factorizations for an arbitrary Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show that there exists such a factorization for any chain of nested subgroups of the Abelian group Zn1×...

nowadays, radar systems have many applications and radar imaging is one of the most important of these applications. inverse synthetic aperture radar (isar) is used to form an image from moving targets. conventional methods use fourier transform to retrieve doppler information. however, because of maneuvering of the target, the doppler spectrum becomes time-varying and the image is blurred. joi...

in this paper, we propose a new residual analysis method using fourier series transform into fuzzy time series model for improving the forecasting performance. this hybrid model takes advantage of the high predictable power of fuzzy time series model and fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...