In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉x...In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.展开更多
We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform bu...We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.展开更多
文摘In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.
文摘We show asymmetric multi-channel sampling on a series of a shift invariant spaces ∑a^m=1v（φ（ta）） with a series of Riesz generators ∑a^m=1φ（ta） in L2（R）, where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between ∑a^m=1v（φ（ta））and L2[0, 2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on ∑a^m=1v（φ（ta））.
