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.

Apparatus for and method of processing image and information recording medium

Abstract: An image processing apparatus capable of extracting widely viewed features of an entire image and speedily performing image processing, and a method and an information recording medium for such processing. Image data of an original image is obtained by imaging the entire original image with an image pickup unit at a time. An amplitude distribution of a signal is obtained from the image data by fast Fourier transform performed by a fast Fourier transform section of a signal processing unit. An amplitude replacement section replaces the amplitude distribution with a predetermined function using the distance from a center of a frequency plane as a parameter. An inverse fast Fourier transform section forms an image corresponding to the original image by inverse fast Fourier transform from a phase distribution of points obtained by the fast Fourier transform and from an amplitude distribution obtained by the above-described replacement.

Calculating zernike coefficients from fourier coefficients

Abstract: Systems, methods, and devices for determining an optical surface model for an optical tissue system of an eye are provided. Techniques include inputting a Fourier transform of optical data from the optical tissue system, inputting a conjugate Fourier transform of a basis function surface, determining a Fourier domain sum of the Fourier transform and the conjugate Fourier transform, calculating an estimated basis function coefficient based on the Fourier domain sum, and determining the optical surface model based on the estimated basis function coefficient. The approach is well suited for employing Fourier transform in wavefront reconstruction using Zernike representation.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

Abstract: A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method.

Calculating Detection Probabilities for Systems Employing Noncoherent Integration

Abstract: Cumulative probability distributions that occur in radar and sonar detection problems are calculated directly from the characteristic function by using a Fourier series. The error in the result is controlled by two parameters which can be adjusted to suit the application. The technique is applied to the problem of determining the detection performance of consecutive discrete Fourier transforms (DFTs) for a narrowband Gaussian signal with a rectangular spectrum. Since the characteristic function is used directly in its product form this technique does not suffer from the numerical problems associated with the partial fraction approach. The technique can handle many different problems in a single computational structure making it a valuable tool in system performance studies.

Fractional fourier transform

Abstract: A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.