Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: In this paper, the same rules can be applied to create a new type of fractional-order Fourier transform which results in a smooth transition of a function when transformed between the real and Fourier spaces.
112 citations
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TL;DR: The Schwartz space of rapidly decaying test functions is characterized by the decay of the short-time Fourier transform or cross-Wigner distribution as mentioned in this paper, and a version of Hardy's theorem is proved for the short time Fourier Transform and for the Wigner Distribution.
Abstract: The Schwartz space of rapidly decaying test functions is characterized by the decay of the short-time Fourier transform or cross-Wigner distribution. Then a version of Hardy's theorem is proved for the short-time Fourier transform and for the Wigner distribution.
110 citations
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TL;DR: The generalized Hilbert transform has similar properties to those of the ordinary Hilbert transform, but it lacks the semigroup property of the fractional Fourier transform.
Abstract: The analytic part of a signal f(t) is obtained by suppressing the negative frequency content of f, or in other words, by suppressing the negative portion of the Fourier transform, f/spl circ/, of f. In the time domain, the construction of the analytic part is based on the Hilbert transform f/spl circ/ of f(t). We generalize the definition of the Hilbert transform in order to obtain the analytic part of a signal that is associated with its fractional Fourier transform, i.e., that part of the signal f(t) that is obtained by suppressing the negative frequency content of the fractional Fourier transform of f(t). We also show that the generalized Hilbert transform has similar properties to those of the ordinary Hilbert transform, but it lacks the semigroup property of the fractional Fourier transform.
108 citations
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TL;DR: The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates.
Abstract: The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary. An important special case also considered is the linear (unattenuated) Radon transform (LRT). The solution is on the form of an orthogonal function expansion matched to projections that are in parallel-ray geometry. This property allows for efficient and accurate processing of the projections with fast Fourier transform (FFT) without interpolation or beam matching. The algorithm is optimized by the use of boundary conditions on the 2-D Fourier transform of the sinogram. These boundary conditions imply that the signal energy of the sinogram is concentrated in well-defined sectors in transform space. The angle defining the sectors depends in a direct way on the radius of the field view. These results are also obtained for fan-beam geometry and the linear Radon transform (the Fourier-Chebyshev transform of the sinogram) to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates. >
107 citations
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107 citations