Introducing Echo: send text notes by sound

p = squash(Σ_i w_i · stretch(p_i))

stretch(p) = ln(p1 − p)

P_i = B_ii < K

P_i = ⊕_{j ∈ S_i} B_ji ≥ K

Δf = 480001024 = 46.875 Hz

ρ = ⟨x, chirp⟩‖x‖ · ‖chirp‖

H₀(k) = Y(k)T(k)

z = YĤ

LLR = (d₁² − d₀²) · |Ĥ|²

C = Σ_k Δf · log₂(1 + SNR_k)

T ≥ SC

Σ_x 2^−ℓ(x) ≤ 1

1r − 1