Next: Historical Notes Up: The Chirplet Transform: Previous: The Chirplet Transform: . ... One of these TF methods, the short-time Fourier transform (STFT), has been used extensively for analyzing speech, music, and other non-stationary signals. ... Another time-frequency representation (which might more appropriately be called a time-scale representation) is the well-known wavelet transformheil-walnut,mallat:theory,daubechies:transform,strangwavelets. ... Historical Notes . ...

Program: TRANSFORM Purpose: Transform a (sub)set using rotation, scaling, translation etc. ... This set will be transformed to OUTSET=, using a concatenation of simple operations like rotation, scaling, translation etc. ... POS= Enter position of centre: [0,0] All operations are defined with respect to a central point. ... If, for example, you want to rotate an object about its centre, then determine the position of this centre (e.g. -6.2 8.5) and enter these numbers here (e.g. POS= -6.2 8.5). ...

Next: Examples of Wavelets Up: The Wavelet Transform Previous: Introduction . The Morlet-Grossmann definition of the continuous wavelet transform [ 17 ] for a 1D signal is: . where denotes the complex conjugate of z , is the analyzing wavelet, a ( >0 ) is the scale parameter and b is the position parameter. ... The last property makes the wavelet transform very suitable for analyzing hierarchical structures. ... Now consider a function which is the wavelet transform of a given function . ...

... Circle rotations. ... Symbolic dynamical systems: sequence spaces, Markov chains, adding machines. Birkhoff recurrence theorem. ... Tent map. ... Expanding maps of a circle. ... Topological entropy. ... Finiteness of entropy for Lipschitz self-maps. Entropy for symbolical dynamical systems. ... Entropy for one-dimensional maps. Entropy for expanding maps and the Misiurewicz-Przytycki theorem. ... Structural stability of expanding circle maps. ... SRB measures for expanding maps. ...

... Image formation is typically described as a linear process. ... where, for 2-dimensional systems, the object coordinates are and the image coordinates are . Such a general description of a linear system is termed shift-variant, because the shape of , the impulse response (or point spread function, PSF), might change as the object position, , is shifted. ... Hence, the exit pupil geometry changes with field position, so the system response changes with field position (i.e., is shift-variant). ...