Band Selective Excitation and \(\frac{\pi }{2}\)-Rotation using Fourier Synthesis

Band selective excitation is widely used in high resolution nuclear magnetic resonance (NMR) spectroscopy to suppress unwanted signals. This article proposes a simple and versatile approach to design such pulses to band selectively rotate the magnetization vector for a desired flip angle. A \(90^\circ \) excitation pulse is designed by amplitude modulation obtained using Fourier series to bring the magnetization vector to the equator of the Bloch sphere. However, this excited magnetization vector is dispersed linearly on the equator with the offset frequency. \(180^\circ \) hard pulses with a free evolution period are used to refocus the excited magnetization vector. The main advantages of this design are overall simplicity and analytical tractability, making it suitable for practical applications. Simulation for band selective excitation and band selective \(\frac{\pi }{2}\)-rotation are presented to validate the theory. Experimental realization of the proposed pulse sequences is done on a 750 MHz spectrometer for a sample of \(99.5\%\ \text {D}_2\text {O}\) and \(0.5\%\ \text {H}_2\text {O}\).