## Modern Mathematical Methods for Signal Processing in Audio and Acoustics

* Presenting author

Abstract:
Signal processing is a key technology that forms the backbone of important developments like MP3, digital television, mobile communications, and wireless networking and is thus of exceptional relevance to economy and society in general. The main goal of this contribution is to give an overview over modern mathematical methods for signal processing in audio and acoustics. In particular, we will address frame theory, time-frequency analysis, as well as compressive sensing and sparsity.The mathematical concept of frames establishes a theoretical background for signal processing. They can give more freedom for the analysis and modification of information and are thus of utmost importance for accurate models of real-world phenomena. Compressive sensing has been one of the major developments in applied mathematics in the past 15 years. The key to its success is that it allows one to exploit signal structure, such as sparsity, to circumvent the traditional barriers of sampling theory. In addition, efficient algorithms allow the practical realization of this theory. Since many real-world signals can be well approximated by an expansion that has only a small number of non-vanishing terms (sparse representation) it has proven a strong potential for many applications including audio and acoustics.