[ENH] Extension of Room Acoustic Parameters (RAP) from _energy_ratio

[SimonBuechner]

Problem

Several RAP can be computed from _energy_ratio and are not yet implemented. This includes several stage acoustic parameters:

The RIR is $p(t)$, the corresponding Schroeder integral is $E(t) = \int_t^{\infty} p^2(\tau)d\tau = \int_0^{\infty} p^2(\tau) d\tau - \int_0^{t} p^2(\tau) d\tau$

Stage Support $ST_{early}$

$$ ST_{early} = 10\log_{10} \frac{\int_{0.02}^{0.1} p^2(t),dt} {\int_{0}^{0.01} p^2(t),dt} =10\log_{10}\frac{E(0.02)-E(0.1)}{E(0)-E(0.01)} $$

Required values

• $E(0)$
• $E(0.01)$
• $E(0.02)$
• $E(0.1)$

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Stage Support $ST_{late}$

$$ ST_{late} = 10\log_{10} \frac{\int_{0.1}^{1.0} p^2(t),dt} {\int_{0}^{0.01} p^2(t),dt} =10\log_{10}\frac{E(0.1)-E(1.0)}{E(0)-E(0.01)} $$

Required values

• $E(0)$
• $E(0.01)$
• $E(0.1)$
• $E(1.0)$

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Center Time $T_s$

Definition:

$$ T_s = \frac{\int_0^\infty t,p^2(t),dt} {\int_0^\infty p^2(t),dt} $$

Using the EDC identity:

$$ T_s = \frac{\int_0^\infty E(t),dt}{E(0)} $$

Discrete form:

$$ T_s = \frac{\sum_n E[n]\Delta t}{E[0]} $$

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This might be extended by the following stage acoustic parameters revolving around strength:

• Strength without direct sound: $G_{7-\infty}$
• Strength without direct sound and late reflections: $G_{7-50}$
• "Strength Early": $G_{Early}$
• "Strength Late": $G_{Late}$

Which may be added later.