In the world of quantum computing, the Hilbert space dimension—the measure of the number of quantum states that a quantum computer can access—is a prized possession. Having a larger Hilbert ...

The concept of a general signal space based on multidimensional linear spaces is developed and applied to the representation of discrete and continuous signals and to linear transformations. Fourier, ...

Introduces methods of complex variables, contour integration, and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms, ...

Hilbert Transform: An integral transform that extracts the harmonic conjugate of a function, crucial for obtaining its analytic representation and for signal processing applications. Fourier ...

Publications of the Astronomical Society of the Pacific, Vol. 110, No. 752 (October 1998), pp. 1205-1215 (11 pages) ABSTRACT We describe a concept for an imaging spectrograph for a large orbiting ...

Hilbert transforms (HT) and analytic signals. Bilateral Laplace transforms (LT): convergence properties. Contour integration methods applied to FT, HT and LT. Discrete-time Fourier series and Fourier ...