As a result of a major program of spectral observations using the CAT 1.4 m telescope and Coude Echelle Spectrograph at ESO, La Silla, 68 high resolution profiles of the 3968.5 A Ca H resonance line have been obtained for 16 late type stars (dwarfs and subgiants, including the sun) ranging from F9 to K5, selected to be representative of a wide span of chromospheric activity. The methods, and results of a set of reduction and analysis techniques applied to these spectra are presented. Each wavelength scale is converted to a frame at rest with respect to the photosphere of the star, and the flux scale is finally transformed into units of absolute flux. A major effort was applied to quantify the effects of the tilted baselines of the recorded spectra on these absolute flux calibrations. The calibrated profiles are used to extract and tabulate measured chromospheric H emission fluxes and the velocity shifts with respect to the photosphere of the emission cores and of the H3 self-reversals.