Applets of Integral and Discrete Transforms

Lectures:
Introduction to integral transforms. Linear spaces, norm, scalar product. Hilbert space. Convergence of series and integrals. Orthogonal systems, series and function convolutions.
Laplace and Fourier transforms. Inverse transforms. Fourier-Laplace transform.
Discrete transforms. Discrete L-transform (Dirichlet series). Discrete Fourier transform. Discretization errors. FFT algorithm.
Distribution, Dirac's impuls, L-image, F-image of distribution. Distribution reprezentation. Convolution as a general integral transform. Inverse convolution. Decomposition. Window function.
Introduction to harmonic analysis. Shanonn-Kotelnik theorem. Mathematical filters, Gabor's transform. Window Fourier transform. Regularization.
Generalized Fourier series and wavelets (time-frequency analysis). Wavelet bases, properties, construction. Continuous wavelet transform. Discrete wavelet transform. Multiresolution decomposition (MRA).
Pyramid's algorithm. Packet decomposition. Data compression, signal reconstruction and other applications.
Software for discrete transforms.