theorem BooleanFourier.fourierCoeff_noiseOperator {n : ℕ} (ρ : ℝ) (f : (Fin n → Bool) → ℝ) (S : Finset (Fin n)) : fourierCoeff (noiseOperator ρ f) S = ρ ^ S.card * fourierCoeff f S

theorem BooleanFourier.noiseOperator_comp {n : ℕ} (ρ σ : ℝ) (f : (Fin n → Bool) → ℝ) : noiseOperator ρ (noiseOperator σ f) = noiseOperator (ρ * σ) f