Calculates the total perceived loudness in Sones based on the specific speech spectrum and hearing thresholds of the patient.
get_specific_loudness(x)A numeric value representing the total loudness in Sones.
An object of class SII.
The current implementation uses a first-order heuristic model of recruitment based on Stevens' Power Law, mapped over an estimated dynamic range. While it is computationally fast and demonstrates the restoration of loudness conceptually, it is not a full psychoacoustic model (like Moore-Glasberg / CAM2Q), as it does not calculate basilar membrane excitation patterns via RoEx filters.
Mathematical Formula:
1. Uncomfortable Loudness Level (UCL) is predicted from the threshold ($T_i$): $$UCL_i = 100 + 0.25 \times \max(0, T_i - 20)$$
2. Dynamic Range (DR): $$DR_i = \max(1, UCL_i - T_i)$$
3. Sensation Level (SL) of speech peaks (RMS + 15 dB): $$SL_i = \max(0, E_i + 15 - T_i)$$
4. Loudness Level (Phons) modeling recruitment: $$Phons_i = \left( \frac{SL_i}{DR_i} \right) \times 100$$
5. Specific Loudness (Sones) per band via Stevens' Power Law: $$Sones_i = 2^{\frac{Phons_i - 40}{10}} \quad \text{for } Phons_i \ge 40$$ $$Sones_i = \left(\frac{Phons_i}{40}\right)^{2.5} \quad \text{for } Phons_i < 40$$
6. Total Loudness (Sones): $$Sones_{Total} = \sum Sones_i \times \text{calibration\_factor}$$
The calibration factor (0.25 for 21 critical bands) is scaled dynamically based on the number of frequency bands used in the underlying SII method (e.g., 21 for critical, 6 for octave) to ensure equivalent loudness summation across different resolutions.