Figure 22

Time-frequency maps of energy density of a 500-points simulated signal (e), the same as in Figure 7, composed of four sine-modulated Gaussians, i.e. Gabor functions (a-b), sine wave and one-point discontinuity (c) and sine wave with linear frequency modulation-chirp (d). Distribution (f) was obtained from a single decomposition in a large (2 * 10⁶ waveforms) dictionary: signal is described by only 30 functions, but changing frequency of the chirp is represented as a series of functions, since in the Gabor dictionary we have only constant frequency modulations. (g) presents average of 100 decompositions of the same signal in different realizations of smaller (5 * 10⁴ atoms) stochastic dictionaries. This smoothes the representation of the chirp, but underlying parametrization is no more compact, (h)-the same as (g), presented in 3 dimensions. Square root of energy proportional to the height of the surface or "temperature" on 2-dimensional plots. [22]