Fourier series are not just integrals; they are geometric projections
In short: Move past the intimidating calculus of Fourier series to see the underlying geometry. This video explains how complex signals are actually just vectors being broken down into simpler components using the principles of linear algebra.
While many students first encounter Fourier series as a dense collection of integrals, Dr. Trefor Bazett reveals a more intuitive framework rooted in linear algebra. The core concept is that computing a Fourier series is essentially the process of decomposing a vector into an orthonormal basis.
By viewing signals through this lens, familiar concepts like linear independence, inner products, and projections become the primary tools for understanding frequency. This perspective transforms a computational hurdle into a clear geometric visualization of how information is structured.
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- Summary by Intellect · source: The beautiful geometric view of FOURIER SERIES // The Linear Algebra Perspective
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