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 )
| Â | \(\mathrm{WPMF}^{(c)}_{k}\) 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 |