# Computation of Psycho-Acoustic Annoyance Using Deep Neural Networks
## 2 Psycho-Acoustic Annoyance Model
### [PERSON]'s Psycho-Acoustic Annoyance Model  
Psycho-acoustic parameters allow us to quantify the degree of subjective discomfort (or pleasantness), in terms of objective metrics that certain sounds produce in people. The [PERSON]'s annoyance model [9] uses 4 psycho-acoustic parameters: Loudness (\(L\)), Sharpness (\(S\)), Fluctuation Strength (\(F\)) and Roughness (\(R\)) to calculate a general annoyance parameter (\(PA\)).  
This model is based on the anatomy of the human ear, which behaves like a bank of filters implemented in the cochlea, the sensory organ of hearing located within the inner ear. Thus, the frequency spectrum of psycho-acoustic metrics is analyzed in terms of _critical bands_[16] with a frequency bandwidth matching the response of the mentioned auditory filters. Sound stimuli that are very close to each other in terms of frequency are combined in the human ear in the same critical band. Serializing these critical bands, we create two different frequency scales, the Bark scale and the ERB scale, called _critical band rate scales_, one measured in _Barks_ and the other one measured in _Equivalent Rectangular Bandwidth_ (_ERBs_) [9].  
Table 1 summarizes the parameterized formulas used for calculating the psycho-acoustic metrics [9] involved in [PERSON]'s model. In the following, we briefly describe the parameters involved in the computation. For further details on each one, the reader is referred to [9].  
* Psycho-acoustic Annoyance (\(PA\)) is a perceptual attribute that allows an objective quantification of noise annoyance from the physical characteristics of the signal, based on the mean values of \(L\), \(S\), \(R\), and \(F\).  
* Loudness (\(L\)) is a perceptual measure of the effect of the energy content of sound on the ear (intensity sensation), measured in _Sones_ using a linear scale. It is standardized in ISO 532B. The process used to calculate \(L\) is based on the Specific Loudness (\(L^{\prime}(z)\) or \(L\) contribution for the \(z\)-th critical band, measured in _Sone/Bark_. The total \(L\) is the result of accumulating all contributions across the different bands, weighted by their specific bandwidth \(\Delta z\).
* Sharpness (\(S\)) is a value of sensory human perception of unpleasantness in sounds that is caused by high frequency components. It is measured in _Aures_ in a linear scale.
* Roughness (\(R\)) describes the perception of the sound fluctuation even when \(L\) or \(L_{eq,T}\) (i.e., the equivalent continuous sound level) remains unchanged. It analyzes the effects with different degrees of frequency modulations (around 70 Hz) in each critical band. The basic unit for \(R\) is _Aper_. For each _ERB_, \(g(z)\) is an arbitrary weighting function, \(m\) is the modulation depth of each _ERB_ and \(k\) is the cross-correlation between the envelopes of the \(ERB\) with indexes \(i\) and \(i-2\).
* Fluctuation Strength (\(F\)) describes how strongly or weakly sounds fluctuate. It depends on the frequency and depth of the \(L\) fluctuations, around 4 Hz in each _ERB_. It is measured in _Vacils_.  
The terms \(C_{S}\), \(C_{R}\) and \(C_{F}\) are calibration constants.