Figure 5

WRSEs as amplitude-noise filters. \(\mathrm{WRSE}_{k}\) amplitude noise filter characteristics, \(k\in\{1,3,7,15,31\} \). (a) Modulation profiles of \(\mathrm{WRSE}_{k}\) sequences. Amplitude modulation involves switching the sign \(\pm\Omega_{0}\); this is equivalent to holding \(\Omega_{0}\) constant and instead shifting the phase \(\phi_{0}\) by π, indicated by the hatching. (b) Corresponding amplitude filter-transfer functions \(F_{{\Omega }}(\omega)\), showing filter order increases with Hamming weights \(r(k)\in\{1,2,3,4,5\}\).