Analysis

Learn Integral Transforms

What a transform actually is, the region of convergence and Bromwich inversion, the heat semigroup, Poisson summation and Paley-Wiener, the radial family of Hankel, Abel and Radon, exact transforms over finite groups and finite fields, and the time-frequency distributions.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Integral Transforms

What a transform isTwo-sided Laplace and the region of convergenceInverting Laplace: the Bromwich contourThe Gauss-Weierstrass transformThe Poisson summation formulaPaley-Wiener: support and analyticityThe Hankel transformThe Abel transformThe Radon transform and tomographyThe Riesz transformFourier analysis on finite abelian groupsThe number-theoretic transformThe Hartley transformChirp-z and Bluestein's algorithmThe fractional Fourier transformThe Wigner-Ville distributionThe cepstrumThe Stieltjes transform
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Integral Transforms exactly where it's useful.

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