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Table 1 Filter characteristics of \(\pmb{\mathrm{WPMF}^{(c)}_{k}}\) constructions corresponding to well-known NMR sequences, SK1 and P2, originally designed to compensate for static amplitude errors to first and second Magnus order respectively (Section  4.3 )

From: Walsh-synthesized noise filters for quantum logic

  \(\mathrm{WPMF}^{(c)}_{k}\) construction Amplitude errors
k \(\mathcal {M}(k)\) \(\vec{\boldsymbol{\phi}}\) \(Y_{k}(\theta)\) (μ − 1) (p − 1)
SK1(θ) 1 2 \(Y_{1}(\theta )\operatorname {PAL}_{1}\) cos−1(−θ/4π) 1 1
P2(θ) 3 4 \(Y_{3}(\theta )\operatorname {PAL}_{3}\) cos−1(−θ/8π) 2 1