Search results for "Discrete-time Fourier transform"

Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform

2014

Localization operators in the discrete setting are used to obtain information on a signalffrom the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.

An attempt to realise the constrained search approach in the density functional theory

2001

Abstract The problem of reconstruction of wave functions from a given electron density is considered. A reformulation of the problem is proposed which is based on the Fourier transform. Arising mathematical problems are studied, namely, the properties of reduced spatial densities and their Fourier images are obtained, which follow from known properties of the wave functions. The proposed approach may provide a practical implementation of the Constrained Search Approach to the DFT.

Performance analysis of optical imaging systems based on the fractional fourier transform

1998

Some image quality parameters, such as the Strehl ratio and the optical transfer function, are analysed in the generalized phase-space, or x-p domain, of the fractional Fourier transform associated with a modified one-dimensional pupil function. Some experimental results together with computer simulations are performed which illustrate the tolerance to defocus of different apertures.

Fractional Fourier Transforms and Geometrical Optics

2010

Discrete wavelet transform implementation in Fourier domain for multidimensional signal

2002

Wavelet transforms are often calculated by using the Mallat algorithm. In this algorithm, a signal is decomposed by a cascade of filtering and downsampling operations. Computing time can be important but the filtering operations can be speeded up by using fast Fourier transform (FFT)-based convolutions. Since it is necessary to work in the Fourier domain when large filters are used, we present some results of Fourier-based optimization of the sampling operations. Acceleration can be obtained by expressing the samplings in the Fourier domain. The general equations of the down- and upsampling of digital multidimensional signals are given. It is shown that for special cases such as the separab…

Teaching Fourier optics through ray matrices

2005

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics prov…