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)
Digital Signal Processing I
Basic signal processing concepts, Fourier analysis and filters. This module can
be used as a starting point or a basic refresher in elementary DSP
Digital Signal Processing II
Adaptive signal processing, A/D and D/A. This module provides the basic
tools for adaptive filtering and a solid mathematical framework for sampling and
quantization
Digital Signal Processing III
Advanced topics: this module covers real-time audio processing (with
examples on a hardware board), image processing and communication system design.
Digital Signal Processing IV
Advanced topics: this module covers real-time audio processing (with
examples on a hardware board), image processing and communication system design.
Instructors (3)
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