We consider a hydrogen atom in a strong static electric field with a weak parallel radio-frequency (rf) field. We compute the photoabsorption spectrum by calculating the spectrum of Floquet states, including their quasienergies and their oscillator strengths. Our calculation is based upon “semiquantal” formulas: we calculate the discrete spectrum of quasienergy states by using a quantum adiabatic approximation combined with semiclassical (Bohr-Sommerfeld) quantization rules. We express this spectrum in a manner consistent with the method of scaled-variable spectroscopy, and then calculate the Fourier transform. These calculated absorption spectra and recurrence spectra are in good agreement with experiments on Li atoms. Additional approximations show that the recurrence spectrum is approximately equal to the product of the recurrence spectrum in a static field times an envelope function. That envelope function is the Fourier transform of a cluster of sidebands surrounding a progenitor level in the rf field. The resulting formula agrees with the low-frequency limit of a formula obtained from a semiclassical treatment.