In the paper an audio compression algorithm based on modeling an audio signal by a partial solution of a certain difference equation in the time domain is investigated. The signal is modeled as a sum of exponentially damped sinusoids. Such an approach is thought to be efficient in modeling the transient segments that are present in speech audio signals and audio signals generated by conventional musical instruments. In order to approximate an audio signal frame with a solution of a difference equation, a variational (STLS) problem is solved using the inverse iteration algorithm with an updating inverse matrix. The α-version of the audio codec based on the STLS-ESM scheme was created and tested in comparison with LAME MP3 codec.