Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.

Double-image encryption based on the affine transform and the gyrator transform

Abstract: We propose a kind of double-image-encryption algorithm by using the affine transform in the gyrator transform domain. Two original images are converted into the real part and the imaginary part of a complex function by employing the affine transform. And then the complex function is encoded and transformed into the gyrator domain. The affine transform, the encoding and the gyrator transform are performed twice in this encryption method. The parameters in the affine transform and the gyrator transform are regarded as the key for the encryption algorithm. Some numerical simulations have validated the feasibility of the proposed image encryption scheme.

Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain

Abstract: Shift-invariant spaces play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. A special class of the shift-invariant spaces is the class of sampling spaces in which functions are determined by their values on a discrete set of points. One of the vital tools used in the study of sampling spaces is the Zak transform. The Zak transform is also related to the Poisson summation formula and a common thread between all these notions is the Fourier transform. In this paper, we extend some of these notions to the fractional Fourier transform (FrFT) domain. First, we introduce two definitions of the discrete fractional Fourier transform and two semi-discrete fractional convolutions associated with them. We employ these definitions to derive necessary and sufficient conditions pertaining to FrFT domain, under which integer shifts of a function form an orthogonal basis or a Riesz basis for a shift-invariant space. We also introduce the fractional Zak transform and derive two different versions of the Poisson summation formula for the FrFT. These extensions are used to obtain new results concerning sampling spaces, to derive the reproducing-kernel for the spaces of fractional band-limited signals, and to obtain a new simple proof of the sampling theorem for signals in that space. Finally, we present an application of our shift-invariant signal model which is linked with the problem of fractional delay filtering.

The Discrete Fourier Transform, Part 4: Spectral Leakage

Abstract: This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). We demonstrate an approach to mitigating spectral leakage based on windowing. Windowing temporally isolates the Short-Time Fourier Transform (STFT) in order to amplitude modulate the input signal. This requires that we know the extent, of the event in the input signal and that we have enough samples to yield a sufficient spectral resolution for our application. This report is a part of project Fenestratus, from the skunk-works of DocJava, Inc. Fenestratus comes from the Latin and means "to furnish with windows".

Quantum fast fourier transform and quantum computation by linear optics

Abstract: Using the quantum fast Fourier transform in linear optics the input mode annihilation operators {a0,a1,...,as−1} are transformed into output mode annihilation operators {b0,b1,...,bs−1}. We show how to implement experimentally such transformations based on the Cooley-Tukey algorithm, by the use of beam splitters and phase shifters in a linear optical system. Optical systems implementing 1,2, and 3 qubits discrete Fourier transform (DFT) are described, and a general method for implementing the n-qubit DFT is analyzed. These transformations are used on various input radiation states by which phase estimation and order finding can be computed.