This lecture introduces the Discrete Fourier Transform (DFT) and its definition using the Fourier Basis for Complex Numbers. It covers the basis expansion in both signal and vector notations, the analysis and synthesis formulas, and the change of basis in matrix form. The lecture also explains the N-point signal representation in the frequency and time domains.
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Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.
Covers the theory of numerical methods for frequency estimation on deterministic signals, including Fourier series and transform, Discrete Fourier transform, and the Sampling theorem.
