Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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10 Jan 2005
TL;DR: In this article, a three-dimensional wave packet generated by a local disturbance in a hypersonic boundary layer flow is studied with the aid of the previously solved initial value problem, and the solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of discrete and continuous modes.
Abstract: A three-dimensional wave packet generated by a local disturbance in a hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of discrete and continuous modes. A specific disturbance consisting of an initial temperature spot is considered, and the receptiv ity to this initial temperature spot is computed for both the twodimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, we numerically compute the inverse Fourier transform. The two-dimensional inverse Fourier transform is found for Mode S, and the result is compared with the asymptotic approximation of the Fourier integral. Due to the synchronism between Mode F and entropy/vorticity modes, it is necessary to d eform the path of integration around the associated branch cut. Additionally, the inverse Fourier transform for a prescribed spanwise wave number is computed for three-dimensional Mode S. Nomenclature A = vector function (direct problem) j A = j th component of vector A B = vector function (adjoint problem) j B = j th component of vector B
6 citations
TL;DR: It is shown that the biorthogonal compactly supported wavelets adapted to a sum of differential operators with constant coefficients are closely connected with the representation of the null-space of the adjoint operator by the corresponding scaling functions.
Abstract: In this paper, we present an explicit method to construct directly in the x-domain compactly supported scaling functions corresponding to the wavelets adapted to a sum of differential operators with constant coefficients. Here the adaptation to an operator is taken to mean that the wavelets give a diagonal form of the operator matrix. We show that the biorthogonal compactly supported wavelets adapted to a sum of differential operators with constant coefficients are closely connected with the representation of the null-space of the adjoint operator by the corresponding scaling functions. We consider the necessary and sufficient conditions (actually the Strang–Fix conditions) on integer shifts of a compactly supported function (distribution) f ∈ S'(ℝ) to represent exactly any function from the null-space of a sum of differential operators with constant coefficients.
6 citations
TL;DR: A real-time FPGA implementation of the blending algorithm, using 2D non-separable systolic filtering scheme, that does not require hardware multipliers and it is able to achieve very high operating frequencies.
Abstract: Creating panoramic images has become a popular feature in modern smart phones, tablets, and digital cameras. A user can create a 360 degree field-of-view photograph from only several images. Quality of the resulting image is related to the number of source images, their brightness, and the used algorithm for their stitching and blending. One of the algorithms that provides excellent results in terms of background color uniformity and reduction of ghosting artifacts is the multi-band blending. The algorithm relies on decomposition of image into multiple frequency bands using dyadic filter bank. Hence, the results are also highly dependant on the used filter bank. In this paper we analyze performance of the FIR filters used for multi-band blending. We present a set of five filters that showed the best results in both literature and our experiments. The set includes Gaussian filter, biorthogonal wavelets, and custom-designed maximally flat and equiripple FIR filters. The presented results of filter comparison are based on several no-reference metrics for image quality. We conclude that 5/3 biorthogonal wavelet produces the best result in average, especially when its short length is considered. Furthermore, we propose a real-time FPGA implementation of the blending algorithm, using 2D non-separable systolic filtering scheme. Its pipeline architecture does not require hardware multipliers and it is able to achieve very high operating frequencies. The implemented system is able to process 91 fps for 1080p (1920 x 1080) image resolution.
6 citations
6 citations
13 Nov 1994
TL;DR: The selection is considered of scaling functions for optimal signal representation by multidimensional biorthogonal wavelet frames by aiming at the minimization of the mean-square approximation error at each level of the decomposition.
Abstract: The selection is considered of scaling functions for optimal signal representation by multidimensional biorthogonal wavelet frames. Criterion for optimality is the minimization of the mean-square approximation error at each level of the decomposition. Conditions are given under which the approximation error of the decomposition approaches zero as the level increases. Optimal and suboptimal families of filters for the realization of the scaling functions are explicitly defined. >
6 citations