In broadband NMR spectroscopy excitation with pseudorandom binary amplitude or phase modulation permits the distribution of the excitation power over the entire data acquisition time while peak power requirements are kept low. For sufficiently low excitation power, the magnetization is the linear response of the spin system to its input. The transfer function of the linearly driven system is recovered with the fast Hadamard transform. It is identical to the FID signal in FT NMR. Increasing excitation levels produce distorted lineshapes resulting from linear processing of a nonlinear spin response. Spectra measured for different degrees of saturation are reproduced faithfully by a numerical solution of the Bloch equations including relaxation during excitation. The origin of the lineshape distortions is discussed on the basis of an expansion of the nonlinear response in terms of the linear response. This expansion is in good agreement with the Bloch equations for limited excitation levels. Its nonlinear response terms are generalized to account for connectivities in coupled spin systems.