# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 2 Monaural Perceptual Effects and Models
### Classic Models for Perceptual Audio Coding
In fact, for the purpose of audio coding it seems far from trivial to come up with a computationally inexpensive measure that is able to correctly quantify a signals' masking ability with respect to its tone- and noise-likeness (\"tonality\"), not only for pure tones or noise but for all types of audio signals. As a remark from the authors, a tonality detection based on modulation spectra [33] would, most likely, be closest to modeling the underlying physiological processes as an algorithm. * Modeling of the HAS _threshold in quiet_
* _Adaptation of the masking threshold_ values computed inside the perceptual model (which is inherently agnostic to the rest of the codec) to the analysis and synthesis framework (mostly filterbank, an associated time/frequency resolution) of the codec. In addition to representing a number of fundamental perceptual effects that are well known from psychoacoustic literature, the described perceptual models also address a number of general practical aspects that are important for use as part of a perceptual audio coder:  
* Both models employ a separate filterbank (Discrete Fourier Transform DFT) for the calculation of the masking effects. Compared to using the critically sampled codec filterbanks, the DFT offers at least two advantages: Firstly, the DFT representation preserves the full energy present in the original signal (rather than that of a subsampled or time-aliased signal version). This is important for an accurate estimation of masking components inside the signal. Secondly, the availability of a magnitude-phase representation plus energy preservation opens the door for computing a plethora of tonality metrics, such as spectral flatness [34] or chaos measure [35]. As a practical consequence of using a DFT for threshold calculation, the calculated masking threshold needs to be adapted (scaled) to the domain of the codecs analysis/synthesis filterbank pair. * In contrast to psychoacoustic experiments, where playback level environment can be controlled very precisely, an audio codec is entirely _agnostic of the playback setup and environment_ following the decoder. As an example, the listener can use the volume adjustment of the playback amplifier at will, and thus play back the same encoded/decoded signal both very softly and extremely loud. Thus, the effect of the codec's _threshold in quiet_ model curve is effectively shifted with the playback volume, and is thus applied far from psychoacoustic reality. Similarly, the audio reproduction system following the decoder may be very imperfect and in practice exhibit significant linear or even non-linear distortions (e.g., small loudspeakers used in mobile devices can have a very uneven frequency response and considerable non-linear distortion). This effectively post-processes the coding noise introduced into the audio signal and may strongly distort the masking situation assumed by the codec. In order to account for this, practical psychoacoustic models for audio coding frequently refrain from attempting to fully model or exploit the effects of known masking phenomena (threshold in quiet, inter-band masking) and are instead conservative in their modeling assumptions in the interest of robustness of audio quality to unknown playback conditions. * While basic psychoacoustic masking effects only depend on the involved audio signals, the perceptual model inside an audio coder needs to adapt its output to the basic properties of the codec system in order to achieve high coding performance. In other words, beyond purely psychoacoustic calculations, properties that interact with the codec algorithms need to be considered, including aspects such as:  
* Time/frequency resolution of analysis/synthesis system Due to the involved analysis/synthesis filterbanks and the coder's block processing structure, the codec system has a certain time/frequency resolution.