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The Fourier series in spectral analysis and function approximation; the Fourier transformation and generalized signals; the Laplace transformation and some of its applications; analog signal processing systems; digitization of analog signals; discrete signals and systems; design of digital filters; the fast Fourier transform and its applications; random signals; finite word-length effects in digital signal processors; selected applications and advanced topics; appendices: function of a real variable, function of a complex variable; references; answers to selected problems.