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Theorems · Theorem · harmonic analysis

ZMod.dft_dft

∀ {N : ℕ} [inst : NeZero N] {E : Type u_1} [inst_1 : AddCommGroup E] [inst_2 : Module ℂ E] (Φ : ZMod N → E),
  ZMod.dft (ZMod.dft Φ) = fun j => ↑N • Φ (-j)

Fourier inversion formula, discrete case.

Defined in
Mathlib.Analysis.Fourier.ZMod
Cited by
3 results in Mathlib
Foundations
Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NeZeroAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZMod.dft_odd_iff · cited by 1ZMod.dft_odd_iffZMod.completedLFunction_one_sub_even · cited by 1ZMod.completedLFunction_o…ZMod.dft_even_iff · cited by 0ZMod.dft_even_iffDFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idAddCommGroup · cited by 12871AddCommGroupComplex · cited by 5565ComplexLinearEquiv · cited by 3317LinearEquivZMod · cited by 1024ZModZMod.dft · cited by 25ZMod.dftZMod.dft_dftCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.