Descriptions of Fourier series windows (FSWs) using multiple coils for in vivo NMR spectroscopy are presented. Spatially dependent phase shifts in experiments implemented with separate transmitter and receiver coils are shown to exist and are theoretically analyzed on and off resonance. With computer simulations, we illustrate the occurrence of unwanted dispersive signals in such experiments. A new approach to the FSW experiment is introduced in which the magnetization is longitudinally modulated and dispersive signals are not produced in experiments executed with multiple transmitter coils. In addition, the longitudinally modulated FSWs avoid localization artifacts due to off resonance excitation within a reasonable chemical-shift range for in vivo 31P spectroscopy.