Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

On the spectral decomposition of stationary time series using walsh functions. II

Abstract: The paper looks at the asymptotic properties of the finite Walsh–Fourier transform applied to a discrete-time stationary time series, and shows that in many ways we have analogous results to those obtained when using the finite trigonometric Fourier transform.

Method and apparatus for remotely calibrating a phased array system used for satellite communication using a unitary transform encoder

Abstract: A method and apparatus for remotely calibrating a system having a plurality of N elements, such as a phased array system, is provided. The method includes generating coherent signals, such as a calibration signal and a reference signal having a predetermined spectral relationship between one another. The calibration signal which is applied to each respective one of the plurality of N elements can be orthogonally encoded using a unitary transform encoder that uses a predetermined transform matrix, such as a Hadamard transform matrix or a two-dimensional discrete Fourier transform matrix, to generate a set of orthogonally encoded signals. The set of orthogonally encoded signals and the reference signal are transmitted to a remote location. The transmitted set of orthogonally encoded signals is coherently detected at the remote location. The coherently detected set of orthogonally encoded signals is then decoded using the inverse of the predetermined encoding matrix to generate a set of decoded signals. The set of decoded signals is then processed for generating calibration data for each element of the phased array system.

Photoacoustic imaging using the Hadamard transform technique.

Abstract: The principles of Hadamard transformation are applied to photoacoustic imaging. The advantages are twofold: reduction of the power density at the sample, and improvement of SNR due to multiplexing advantage. The compatibility of Hadamard with other multiplex transform techniques is discussed.

Hilfer-Hadamard Fractional Differential Equations; Existence and Attractivity

Abstract: This work deals with a class of Hilfer-Hadamard differential equations. Existence and stability of solutions are presented. We use an appropriate fixed point theorem.