This paper presents an experimental modal analysis of a damped multi-degree-of-freedom mechanical system using a continuous wavelet transform. An approximation of the wavelet transform of the impulse response function is deduced, which serves as a basis for the extraction of the natural frequencies, the damping ratios and the mode shapes. Due to an approximation with a finite Taylor series, a computational error in the identified oscillatory amplitude occurs and is observed for the simulated system response. The presented approach of modal identification is applied to real mechanical systems, such as a steel beam and the horizontal tail of an ultralight aircraft. Using the proposed measurement methodology, it is possible to reconstruct the spatial mode shapes of any dynamic linear system with an arbitrary geometry.