Discrete Fourier series: Inherent periodicities and time shifts
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Description
This lecture covers the synthesis and analysis formulas of the Discrete Fourier Transform (DFT), mapping N-periodic signals to N-periodic sequences of Fourier coefficients. It explains how the DFT helps define time shifts for finite-length signals, providing insights into circular shifts and the equivalence between DFS and DFT.
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Covers the theory of numerical methods for frequency estimation on deterministic signals, including Fourier series and transform, Discrete Fourier transform, and the Sampling theorem.
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 Fourier transform, its properties, and applications in signal processing and differential equations, demonstrating its importance in mathematical analysis.
Explores psychoacoustics, signal processing, and the brain's interpretation of sound frequencies, covering topics like the Missing Fundamental phenomenon and the inner workings of the cochlea.
