Ring doves (Streptopelia risoria) produce a "coo" vocalization that is essentially a pure-tone sound at a frequency of about 600 Hz and with a duration of about 1.5 s. While making this vocalization, the dove inflates the upper part of its esophagus to form a thin-walled sac structure that radiates sound to the surroundings. It is a reasonable assumption that the combined influence of the trachea, glottis and inflated upper esophagus acts as an effective band-pass filter to eliminate higher harmonics generated by the vibrating syringeal valve. Calculations reported here indicate that this is indeed the case. The tracheal tube, terminated by a glottal constriction, is the initial resonant structure, and subsequent resonant filtering takes place through the action of the inflated esophageal sac. The inflated esophagus proves to be a more efficient sound radiating mechanism than an open beak. The action of this sac is only moderately affected by the degree of inflation, although an uninflated esophagus is inactive as a sound radiator. These conclusions are supported by measurements and observations that have been reported in a companion paper.