Theorems · Theorem · harmonic analysis
ZMod.dft_even_iff
∀ {N : ℕ} [inst : NeZero N] {Φ : ZMod N → ℂ}, Function.Even (ZMod.dft Φ) ↔ Function.Even ΦThe discrete Fourier transform of Φ is even if and only if Φ itself is.
- Defined in
- Mathlib.Analysis.Fourier.ZMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Moduleproof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidproof · cited by 12,281
- Complexstatement and proof · cited by 5,565
- LinearEquivstatement · cited by 3,317
- ZModstatement and proof · cited by 1,024
- neg_negproof · cited by 960
- Module.IsTorsionFreeproof · cited by 600
- Function.Evenstatement and proof · cited by 36
- ZMod.dftstatement and proof · cited by 25
- smul_right_injproof · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.