Higher‐Order Time‐Frequency Representations

This chapter presents some ideas on the extension of bilinear time‐frequency representations to multilinear representations. Two different approaches are being pursued. The first develops the idea of multi‐spectral analysis of non‐stationary signals and is based on the definition of time‐multifrequency representations. The second approach is more pragmatic and rests on polynomial modulation analysis. This precise framework leads to the development of multilinear time‐frequency representations with perfect concentration on the studied modulation laws; moreover, these representations find their place in a general class of multilinear time‐frequency representations. The chapter ends with a discussion and an opening towards affine multilinear representations.