The first measurements of the spectral distribution of infrared radiation emitted by an undulator are reported. They are compared with calculations including both velocity and acceleration terms. Measurements have been performed at the beam line SIRLOIN (Spectroscopie en InfraRouge Lointain). The agreement between the observations and this first exact numerical solution shows that the inclusion of the velocity term in the submillimeter frequency range is necessary. Moreover, structures due to undulator edges are observed in the far infrared and mid-infrared range, while the interference pattern due to redshifted harmonics of the undulator is dominating in the mid-infrared to near infrared.