Visualization and analysis of modulated pulses in magnetic resonance by joint time-frequency representations

We study the utility of joint time-frequency representations for the analysis of shaped or composite pulses for magnetic resonance. Such spectrograms are commonly used for the visualization of shaped laser pulses in optical spectroscopy. This intuitive representation provides additional insight compared to conventional approaches, which exclusively show either temporal or spectral information. We focus on the short-time Fourier transform, which provides not only amplitude but also phase information. The approach is illustrated for broadband inversion pulses, multiple quantum excitation and broadband heteronuclear decoupling. The physical interpretation and validity of the approach is discussed.