Composite spectrogram using multiple Fourier transforms

The authors propose a time-frequency (T-F) analysis method that uses a time- and frequency-dependent resolution to represent a signal. The method is based on the idea of splitting the T-F plane into equal-TF-area Heisenberg boxes in some optimal way that closely matches spectral events. Compared with existing methods based on orthogonal decompositions, by lifting the orthogonality constraint, extra freedom is gained in the way the T-F plane can be partitioned, which enables time and frequency adaptation at the same time. A best tiling selection algorithm of quadratic complexity is derived using dynamic programming to find the optimal frame from a family. Experiments show the advantage of this more flexible representation.