Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.

Recovery of piecewise smooth images from few fourier samples

Abstract: We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples. Assuming the discontinuity set of the image is localized to the zero level-set of a trigonometric polynomial, we show the Fourier transform coefficients of partial derivatives of the signal satisfy an annihilation relation. We present necessary and sufficient conditions for unique recovery of piecewise constant images using the above annihilation relation. We pose the recovery of the Fourier coefficients of the signal from the measurements as a convex matrix completion algorithm, which relies on the lifting of the Fourier data to a structured low-rank matrix; this approach jointly estimates the signal and the annihilating filter. Finally, we demonstrate our algorithm on the recovery of MRI phantoms from few low-resolution Fourier samples.

Classification of PSK signals using the DFT of phase histogram

Abstract: A method is presented for classifying multi-level PSK signals in the presence of additive white Gaussian noise (AGWN). The technique is based on the Discrete Fourier Transform (DFT) of a phase histogram. The probability of correct classification is given and it is found that the technique performs well at low SNR. The benefits of this technique are that it is simple to implement and requires no prior knowledge of the SNR of the signal for the classification.

Spatial resolution analysis for discrete Fourier transform-based Brillouin optical time domain reflectometry

Abstract: Discrete Fourier transform (DFT) requires many sampled points for a spectrum. We find that the spatial resolution of the DFT-based Brillouin optical time domain reflectometry (BOTDR) is determined by the pulse width of the probe light and the time length of the sampling data used to perform the DFT. The best spatial resolution is limited by the pulse width. At a certain sampling rate, the spatial resolution increases linearly with the number of points in DFT. The frequency uncertainty improves with the increased number. Window function restrains the spectral leakage significantly and can improve the spatial resolution. But when the influence of the spectral leakage can be neglected, the frequency uncertainty without a window function is better than that with a window function for the same spatial resolution.

An accurate discrete Fourier transform for image processing

Abstract: The classical method of numerically computing the Fourier transform of digitized functions in one or in d-dimensions is the so-called discrete Fourier transform (DFT), efficiently implemented as Fast Fourier Transform (FFT) algorithms. In many cases the DFT is not an adequate approximation of the continuous Fourier transform. The method presented in this contribution provides accurate approximations of the continuous Fourier transform with similar time complexity. The assumption of signal periodicity is no longer posed and allows to compute numerical Fourier transforms in a broader domain of frequency than the usual half-period of the DFT. In image processing this behavior is highly welcomed since it allows to obtain the Fourier transform of an image without the usual interferences of the periodicity of the classical DFT. The mathematical method is developed and numerical examples are presented.

Image fusion based on image decomposition using self-fractional Fourier functions

Abstract: Image fusion has been receiving increasing attention in the research community in a wide spectrum of applications. Several algorithms in spatial and frequency domains have been developed for this purpose. In this paper we propose a novel algorithm which involves the use of fractional Fourier domains which are intermediate between spatial and frequency domains. The proposed image fusion scheme is based on decomposition of source images (or its transformed version) into self-fractional Fourier functions. The decomposed images are then fused by maximum absolute value selection rule. The selected images are combined and inverse transformation is taken to obtain the final fused image. The proposed decomposition scheme and the use of some transformation before the decomposition step offer additional degrees of freedom in the image fusion scheme. Simulation results of the proposed scheme for different transformation of the source images for two different sets of images are also presented. It is observed through the simulation results that the use of taking the transformation before the decomposition step improves the quality of fused image. In particular the results of using the fractional Fourier transform and discrete cosine transform before the decomposition step are encouraging.