Analysis

Learn Fourier & Harmonic Analysis

Decomposing signals into frequencies: Fourier series and convergence (Dirichlet, Fejér, Gibbs), the Fourier transform and Plancherel, convolution, the FFT, the uncertainty principle, wavelets, the Dirac delta and distributions, and harmonic analysis on groups.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

30 lessons in Fourier & Harmonic Analysis

Fourier seriesConvergence: Dirichlet, Fejér & GibbsThe Fourier transform & PlancherelConvolution & the convolution theoremParseval, energy & the spectrumThe DFT & the FFTUncertainty & time–frequency analysisWavelets & multiresolutionDistributions & the Dirac deltaAbstract harmonic analysisSampling & the Nyquist–Shannon theoremAliasing & the folding frequencyFrequency bins & resolutionThe z-transform & transfer functionsDigital filters: FIR vs IIRThe Laplace transformWindowing & spectral leakageTwo-dimensional Fourier & imagesPointwise convergence: du Bois-Reymond to CarlesonLittlewood–Paley theoryBochner's theoremProlate functions and the 2WT theoremGabor frames and Balian–LowFilter banks and perfect reconstructionFourier optics: the far fieldPhase retrievalModulation and the frequency-shift theoremBandpass samplingThe Fourier restriction problemWirtinger's inequality and the isoperimetric theorem
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 day its model predicts you would forget it. A short placement check finds what you already know, so you start Fourier & Harmonic Analysis exactly where it's useful.

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