Lecture

The DFT as a change of basis

Description

This lecture introduces the Discrete Fourier Transform (DFT) as a change of basis, highlighting the mathematical setup with finite-length signals and the Fourier Basis for complex numbers. The instructor explains the concept of a change of basis as a change of perspective that can reveal insights, followed by a proof of orthogonality within the basis vectors. The lecture concludes by discussing the implications of having N orthogonal vectors as a basis for CN, emphasizing the need for normalization.

In MOOCs (4)

Instructors (3)

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Official source

https://mediaspace.epfl.ch/media/0_5ah3j5oz

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Information engineering

Signal processing: Fourier analysis

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