Accurate, full-band estimates of teleseismic P Green's functions are recovered using constraints from the autospectra and cross spectra of seismograms generally representing multiple sources and receivers. This advance represents a higher-order refinement of traditional receiver functions that sacrifice structural signals finishing as P energy on a three-component seismogram to approximate the source signature. We estimate the autospectrum of a source signature from the cross correlogram of two seismogram channels that record this same source. Imposing a well-founded assumption on the phase spectrum of the P component of the teleseismic P Green's function, namely, that it is minimum phase, allows the total vector impulse response to be retrieved. We assess the accuracy of this spectral reconstruction approach to the deconvolution problem through synthetic and real data examples.