The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I β«Ψβ¬ 3 2 . Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one-to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse "stimulated echo" sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the "stimulated echo" sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.