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Lecture 9: Fourier Transform Properties

Topics covered: Linearity, symmetry, time shifting, differentiation and integration, time and frequency scaling, duality, Parseval’s relation; Convolution and modulation properties and the basis they provide for filtering, modulation, and sampling; Polar representation, magnitude and phase, Bode plots; Use of transform methods to analyze LTI systems characterized by differential and difference equations; Cascade and parallel form realization: first- and second-order systems.

Instructor: Prof. Alan V. Oppenheim

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