https://novaprd-lb.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 Properties of Clifford-Legendre Polynomials https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:51143 Wed 23 Aug 2023 12:15:35 AEST ]]> Sampling aspects of approximately time-limited multiband and bandpass signals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:28649 Wed 11 Apr 2018 15:36:20 AEST ]]> Circumcentering Reflection Methods for Nonconvex Feasibility Problems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:49115 Tue 30 Apr 2024 09:31:00 AEST ]]> Optimization in the construction of cardinal and symmetric wavelets on the line https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:46751 Tue 29 Nov 2022 15:25:35 AEDT ]]> Pseudo Clifford Bandpass Prolates https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:54550 Tue 27 Feb 2024 20:46:44 AEDT ]]> New Properties of Clifford Prolate Spheroidal Wave Functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:54452 Tue 27 Feb 2024 13:57:20 AEDT ]]> Frame properties of shifts of prolate and bandpass prolate functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32628 Tue 26 Jun 2018 15:47:16 AEST ]]> On the numerical evaluation of bandpass prolates II https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32629 Tue 26 Jun 2018 15:47:16 AEST ]]> Spatio–Spectral Limiting on Replacements of Tori by Cubes https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:54216 Tue 13 Feb 2024 11:57:56 AEDT ]]> Constraint Reduction Reformulations for Projection Algorithms with Applications to Wavelet Construction https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:40664 Thu 28 Jul 2022 11:42:05 AEST ]]> A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:49659 Thu 25 May 2023 16:22:58 AEST ]]> Centering Projection Methods for Wavelet Feasibility Problems https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:49651 Thu 25 May 2023 14:44:45 AEST ]]> Spatio-spectral limiting on Boolean cubes https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:39792 Thu 23 Jun 2022 14:13:06 AEST ]]> Spatio-spectral limiting on discrete tori: adjacency invariant spaces https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:39638 Thu 16 Jun 2022 14:27:16 AEST ]]> Spatio-spectral limiting on redundant cubes: a case study https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:39589 Thu 16 Jun 2022 08:40:38 AEST ]]> Optimization in the construction of nearly cardinal and nearly symmetric wavelets https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:44428 Thu 13 Oct 2022 09:51:38 AEDT ]]> Higher-dimensional wavelets and the Douglas-Rachford algorithm https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:44427 Thu 13 Oct 2022 09:51:31 AEDT ]]> Numerical computation of eigenspaces of spatio-spectral limiting on hypercubes https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:44426 Thu 13 Oct 2022 09:51:25 AEDT ]]> Sampling approximations for time- and bandlimiting https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:10487 Sat 24 Mar 2018 08:09:15 AEDT ]]> Letter to the editor: on the numerical evaluation of bandpass prolates https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:19894 Sat 24 Mar 2018 07:57:02 AEDT ]]> Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:5884 Sat 24 Mar 2018 07:49:15 AEDT ]]> Sampling and time-frequency localization of band-limited and multiband signals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:6746 Sat 24 Mar 2018 07:47:29 AEDT ]]> Frame properties of shifts of prolate spheroidal wave functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:26780 Sat 24 Mar 2018 07:36:21 AEDT ]]> Prolate shift frames and their duals https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:26389 Ω of square-integrable functions bandlimited to [-Ω/2, Ω/2] generated by translates φn (t - αℓ) of prolate spheroidal wave-functions φn (where α > 0 and ℓ is an integer). We estimate frame bounds and give a Fourier construction of the dual frames. An ℓ2 estimate on the decay of uniform samples of prolate functions is given to show that the computation of the duals can be done efficiently.]]> Sat 24 Mar 2018 07:33:06 AEDT ]]> Wavelet frames generated by bandpass prolate functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:26390 Sat 24 Mar 2018 07:33:04 AEDT ]]> On the numerical computation of certain eigenfunctions of time and multiband limiting https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:25363 Sat 24 Mar 2018 07:24:40 AEDT ]]> Quaternionic fundamental cardinal splines: interpolation and sampling https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:46621 Bq of quaternionic order q, for short quaternionic B-splines, are quaternion-valued piecewise Müntz polynomials whose scalar parts interpolate the classical Schoenberg splines Bn,n ∈N, with respect to degree and smoothness. They in general do not satisfy the interpolation property Bq(n)=δn,0,n ∈Z. However, the application of the interpolation filter (∑k∈ZBqˆ(ξ+2πk))−1 —if well-defined—in the frequency domain yields a cardinal fundamental spline of quaternionic order that satisfies the interpolation property. We handle the ambiguity of the quaternion-valued exponential function appearing in the denominator of the interpolation filter and relate the filter to interesting properties of a quaternionic Hurwitz zeta function and the existence of complex quaternionic inverses. Finally, we show that the cardinal fundamental splines of quaternionic order fit into the setting of Kramer’s Lemma and allow for a family of sampling, respectively, interpolation series.]]> Mon 28 Nov 2022 10:57:31 AEDT ]]> Bandpass pseudo prolate shift frames and Riesz bases https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32357 PWΩ which is generated by the shifts of prolate spheroidal wave functions, we generate frames (reps. Riesz bases) for the bandpass space, and show that the frame (resp. Riesz) bounds are the same as those of the baseband frame (resp. Riesz basis).]]> Mon 28 May 2018 09:41:01 AEST ]]> Riesz bounds for prolate shifts https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32356 Mon 28 May 2018 09:41:01 AEST ]]> Sampling in Paley-Wiener spaces, uncertainty and the prolate spheroidal wavefunctions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32355 Mon 28 May 2018 09:40:59 AEST ]]> Frame expansions of bandlimited signals using prolate spheroidal wave functions https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:43608 Mon 26 Sep 2022 15:54:45 AEST ]]> Duration and bandwidth limiting: prolate functions, sampling, and applications https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:25783 Mon 23 Jan 2017 16:42:42 AEDT ]]> Non-separable multidimensional multiresolution wavelets: A Douglas-Rachford approach https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:56171 Mon 12 Aug 2024 09:58:12 AEST ]]> An analogue of Slepian vectors on boolean hypercubes https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:36786 Mon 06 Jul 2020 09:53:42 AEST ]]> Quaternionic B-splines https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:32073 Bq of quaternionic order q, defined on the real line for the purposes of multi-channel signal analysis. The functions Bq are defined first by their Fourier transforms, then as the solutions of a distributional differential equation of quaternionic order. The equivalence of these definitions requires properties of quaternionic Gamma functions and binomial expansions, both of which we investigate. The relationship between Bq and a backwards difference operator is shown, leading to a recurrence formula. We show that the collection of integer shifts of Bq is a Riesz basis for its span, hence generating a multiresolution analysis. Finally, we demonstrate the pointwise and Lp convergence of the quaternionic B-splines to quaternionic Gaussian functions.]]> Fri 27 Apr 2018 11:52:51 AEST ]]> Clifford Prolate Spheroidal Wavefunctions and Associated Shift Frames https://novaprd-lb.newcastle.edu.au/vital/access/manager/Repository/uon:54941 Fri 22 Mar 2024 15:28:22 AEDT ]]>