Theory of continuously phased planar sources for sound reinforcement

Open Access

Algorithm 3

Find delay lengths.

procedure CurvinG(x_r0, z₀, H, V, N, η, β, g, a, b)
constant:
Δv = −V/N
Δh = Δv
ν = f(x_r,0, z₀)	according to Eq. (19)
ϑ₀ = ν − η
$M = - \frac{H}{2 Δ v} + 1$ $M=-\frac{H}{2\enspace \Delta v}+1$
$r = \frac{z_{0}}{\sin (η + ϑ_{0})}$ $r=\frac{{z}_0}{\mathrm{sin}(\eta +{\vartheta }_0)}$	according to fig. 2
initialization:
W = zeros(M, N)
Wh = zeros(M, N)
Wv = zeros(M, N)
Wv[1] = −sinϑ₀
Whh = a
for n = 1…N do
W[m,n + 1] ← W[m, n] + Wv[m, n] Δv	num. int.
v = n Δv
r ← f(v, η, Wh[m, n], Wv[m, n], z₀)	cf. Eq. (12)
Wvv ← f(r, g, β, a, b, Wv[m, n])	cf. Eq. (18)
Wv[m, n + 1] ← Wv[m, n] + Wvv Δv	num. int.
end for
for m = 1…M do
for n = 1…N do
W[m + 1, n]←W[m, n] + Wh[m, n] Δh	num. int.
v = n
Δv r ← f(v, η, Wh[m, n], Wv[m, n], z₀)	cf. Eq. (12)
$Whh = \frac{Wh [m, n]^{2}}{r} + a$ ${Whh}=\frac{{Wh}[m,n{]}^2}{r}+a$	cf. Eq. (16)
$Whv = \frac{Wh [m, n] Wv [m, n]}{r} + b$ ${Whv}=\frac{{Wh}[m,n]\enspace {Wv}[m,n]}{r}+b$	cf. Eq. (17)
Wv[m + 1, n] ← Wv[m, n]+Whv Δh	num. int.
Wh[m+1, n] ← Wh[m, n]+Whh Δh	num. int.
end for
end for
return W
end procedure

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