Hyperbolic secant inversion pulses

Hyperbolic Secant Inversion Pulses and Wideband Uniform Rate Smooth Truncation... 

Siegel et al. showed that enhancement of the CT can also be obtained using hyperbolic secant (HS) pulses to invert selectively the STs [74], Unlike the DFS waveform, whose frequency sweep is generated by a constant rf-pulse phase while modulating the amplitude, the HS pulse utilizes both amplitude and phase modulation, yielding an enhancement exceeding that obtained by DFS or RAPT [61, 74, 75]. Most recently, the pulse sequence called wideband uniform-rate smooth truncation (WURST) [76] was introduced to achieve selective adiabatic inversion using a lower power of the rf-field than that required for the HS pulses [77,78]. One of its applications involved more efficient detection of insensitive nuclei, such as 33S [79]. 

From equation (8) three modes of adiabatic spin inversion using RF pulses may be defined as (a) amplitude modulated pulses, e.g. I-BURP [13], G3[16], I-SNOB [17], (b) frequency modulated pulses, e.g. chirp [18,20], tangential sweep [20,21] and (c) both amplitude and frequency modulated pulses, e.g. the hyperbolic secant [22] or WURST (Wide band Uniform Rate Smooth Truncation) [23] pulse. 

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