Applications of seismic impedance inversion normally assume the data are free of multiples and transmission effects, requiring knowledge of the seismic pulse that is assumed to be stationary. An alternative formulation for impedance inversion is based on an exact frequency-domain, zero-offset reflectivity function for a 1D medium. Analytical formulas for the Fréchet derivatives are derived for efficient implementation of an iterative nonlinear inversion. The exact zero-offset reflectivity accounts for internal multiples and transmission effects in the data. Absorption and dispersion are also conveniently handled if a reasonable estimate for the quality (Q) factor of the medium is available. A series of convenient features are included in the inversion algorithm: an automatic estimation of the amplitude spectrum of the seismic pulse, an impedance transform that makes the inversion independent from the initial smooth model, and a practical approach to estimate the regularization weight. Numerical tests using synthetic and real data show that the method is stable and needs only a few iterations to converge.