In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power adaptable and also reversible. Lifting scheme is used to approximate complex multiplications appearing in the FFT lattice struct...

This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper add...

The class of second-order curvilinear gratings consists of all the curvilinear gratings that are obtained by second-order spatial transformations of periodic gratings. It includes, for example, circular, elliptic, and hyperbolic gratings as well as circular, elliptic, and hyperbolic zone plates. Such structures occur quite frequently in optics, and their Fourier transforms may arise, for instan...

We give a discussion of harmonic analysis on finite abelian groups, emphasizing various ways in which the structure of the group is encoded on various spaces of functions, ways in which the Fourier transform detects and preserves these structures. We discuss the major tools, like convolutions and Fourier transforms, along with some fundamental theorems, like the Plancheral, Parseval, Fourier in...

The following paper presents the results of tests conducted by the author in the field of verification of influence of JPEG lossy compression on the robustness of data hiding methods used for the colour image which has been transformed to the frequency domain. The data have been embedded to the Fourier magnitude spectrum of the image. The possibility of decoding the hidden data with two embeddi...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...

We consider brightness/contrast-invariant and rotation-discriminating template matching that searches an image to analyze A for a query image Q. We propose to use the complex coefficients of the discrete Fourier transform of the radial projections to compute new rotation-invariant local features. These coefficients can be efficiently obtained via FFT. We classify templates in “stable” and “unst...

Blinking and eye movement are one of the most important abilities that most people have, even people with spinal cord problem. By using this ability these people could handle some of their activities such as moving their wheelchair without the help of others. One of the most important fields in Human-Robot Interaction is the development of artificial limbs working with brain signals. The purpos...

Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the discrete Fourier transform (DFT) algorithm, compared with fast Fourier transform (FFT) tools. Simulations show that the precision is quite comparable, but in the ...