Mathematicians crack signal-processing equations used in wireless and radar systems
Researchers have solved longstanding mathematical problems that underpin how engineers filter and process signals in telecommunications, audio processing, and radar. The breakthrough makes it faster and more reliable to design systems that remove noise from data — a critical step in everything from 5G networks to medical imaging.
Originaltitel: Norm estimates for a broad class of modulation spaces, and continuity of Fourier type operators
<p>We consider a broad class of modulation spaces M(ω, B),parameterized with weight function ω and a normal quasiBanach function space B of order r0 ∈ (0, 1]. Then we provethat f ∈ M(ω, B), if and only if Vϕf belongs to the Wieneramalgam space Wr(ω, B), and</p><p>∥f∥M(ω,B) ≍ ∥Vϕf · ω∥B ≍ ∥Vϕf∥Wr(ω,B), r ∈ [r0, ∞].</p><p>We use the results to extend and improve continuity andlifting properties for pseudo-differential and Toeplitz operatorswith symbols in weighted M∞,r0 -spaces, r0 ≤ 1, when actingon M(ω, B)-spaces.</p>