# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 2 Monaural Perceptual Effects and Models
### Properties of Monaural Human Hearing  
The principles of the human auditory system and the underlying physiological properties of the ear have been studied by researchers in the field of medicine, biology, and engineering. Comprehensive psychoacoustic studies have been performed and described by [PERSON] [24] and [PERSON] [25], among others. Many psychoacoustic effects can be explained by the physiological properties of the hearing process itself. The outer ear and ear canal collect arriving air pressure waves, which are transmitted as mechanical vibration via the ear drum and inner ear to the liquid-filled cochlea. The cochlea's shape resembles a tapered spiral similar to a coiled snail (the name is derived from the Ancient Greek word for \"snail shell\"). The inner surface of the cochlea is lined by sensory cells consisting of small hairs connected to nerve endings--so-called hair-cells. Depending on the frequency of the incoming sound, different areas of the cochlea resonate, causing the hair-cells at the respective region to vibrate (\"tonotopic organization\"). In turn, the stimulated nerve endings send impulses to the brain, allowing it to perceive and distinguish sounds of different frequency, level, and timbre. Due to these physiological properties of the hearing process, the perception and resolution of frequency is not linear and becomes coarser at higher frequencies. The bandwidth of the auditory filters in the HAS--the so-called \"critical bandwidth\"--describes the bandwidth within which the signal components interact perceptually with each other rather than being perceived as independent from each other. Based on modeling this auditory filter bandwidth, perceptually motivated frequency scales can be derived, such as the Bark-Scale proposed by [PERSON] [25; 26] or the Equivalent Rectangular Bandwidth (ERB)-scale by [PERSON] and [PERSON] [27; 28] (see Figure 2). Figure 2: Critical Bandwidth and resulting perceptual scales, as modeled by the Bark-Scale and Equivalent Rectangular Bandwidth (ERB)-Scale. An important aspect for perceptual audio coding is the consideration of _masking effects_ in the human auditory system, i.e., the effect that louder sounds (\"masker\") tend to suppress the perception of other, weaker sounds (\"probe\") in the masker's spectral or temporal vicinity. A common example for masking is how the sound of a bird (probe) can be drowned by the sound of a car passing by (masker) in human auditory perception. One category of such masking effects is known as \"spectral masking effects\" or \"simultaneous masking\" [25] (see Figure 3), for which the following aspects were observed:  
* A frequency dependent _threshold of hearing in quiet_ describes the minimum sound pressure level (SPL) of a sound to be perceivable in isolation and under extremely quite conditions. * In the presence of a masker, the threshold in quiet curve changes into a masking threshold, which shows a bell-shaped increase in frequencies in the vicinity of the masker, depending on its frequency, level, and signal type. Any sound beneath this threshold is masked by the louder signal, and thus inaudible for the average listener. In perceptual audio coding, the coding error (i.e., the introduced quantization noise) corresponds to the probe signal in this experimental scenario. * Masking effects are strongest for signals that are within the critical bandwidth of the masker. Within the critical bandwidth, the masking threshold remains constant. Furthermore, the masking effects spread to frequencies beyond the critical bandwidth (so-called _inter-band masking_). The upper slope of the masking threshold depends on multiple factors, such as absolute frequency and sound pressure level of the masker, whereas the lower slope hardly shows a level dependency. * Depending on the type of masker, i.e., tone or (narrow-band) noise, the strength of the masking effect varies.