Numerical Computations Using Gabor Frames for Periodic Spaces

نویسنده

  • PETER LEMPEL SØNDERGAARD
چکیده

This thesis presents Gabor frames for L2(T) and for the space of periodic sequences Cp , as being analogue to Fourier series and the discrete Fourier transform. Results from the standard theory of Gabor frames for L2(R) are transferred to the periodic setting. This includes results about sampling Gabor systems and existence of Gabor frames. The interrelation of Gabor frames for the continuous space L2(T) and the discrete space Cp is afterwards used to construct a new method for numerical di erentiation with properties close to the method of spectral di erentiation. Finally, the various results are illustrated by numerical examples.

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تاریخ انتشار 2014