Theorems · Theorem · harmonic analysis
ZMod.dft_odd_iff
∀ {N : ℕ} [inst : NeZero N] {Φ : ZMod N → ℂ}, Function.Odd (ZMod.dft Φ) ↔ Function.Odd ΦThe discrete Fourier transform of Φ is odd if and only if Φ itself is.
- Defined in
- Mathlib.Analysis.Fourier.ZMod
- Cited by
- 1 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- map_negproof · cited by 378
- Function.Oddstatement and proof · cited by 38
- ZMod.dftstatement and proof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.completedLFunction_one_sub_oddproof · cited by 1