# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 4 Models for Parametric Audio Coding
### Parametric Spatial Audio Coding  
The second important class of (hybrid) parametric coding techniques is the family of spatial audio coding algorithms that will be described in this subsection. The forerunner of parametric spatial audio coding algorithms is the _intensity stereo (IS)_ coding approach that was mentioned before under the heading \"coding for stereo signals\" and adheres to the basic framework shown in Figure 6. In the encoder, the spectral values of the left and right channel are downmixed into a single mono channel, plus some directional information that indicates the energy ratio between the two channel signals in each codec frequency band. In the decoder, the transmitted mono signal is scaled differently to calculate left and right output spectral values. This is done using the directional information, such that the original energy (intensity) of both channel signals is preserved (whereas the waveforms come out quite differently due to the downmix/upmix process). As a consequence, intensity stereo is a _lossy joint stereo technique_ independent of any possible quantization-related errors. Both output signals are scaled copies of each other that only _differ in their intensity_ (thus the name of the technique) in each frequency band, just as if they had been created on a mixing console with frequency band-wise dynamic left-right panning controls. This basic technique has been published under different names, including \"intensity stereo\" [60; 61] and \"channel coupling\" [62], and generalizes to multi-channel (i.e., down/upmixing) of several audio channels. Due to the lossy nature and simplicity of the approach, intensity stereo can be applied only to high frequencies (typically above 4 kHz) without unduly degrading the stereo image. Nonetheless, for certain classes of stereo signals with high temporal complexity (e.g., applause), artifacts are introduced due to the limited temporal resolution of the scheme (owing the codec's filterbank and temporal framing design). Consequently, also the use of sophisticated perceptual control mechanisms has been proposed to be advantageous for controlling the technique with a special focus on the signal's fine temporal structure [60; 63]. The next generation of spatial audio coding is the _Parametric Stereo (PS)_ scheme, as described in previous studies [17; 64]. Similar to intensity stereo, it is a 2-1-2 scheme, i.e., two input channels are mixed into one downmix channel, transmitted, and upmixed in the decoder into two output channels. In contrast to intensity stereo, PS has numerous enhancements that allow its use throughout the entire frequency range (at the expense of increased computational complexity):  
* Whereas intensity stereo works on the codec's native spectral representation (with all its constraints regarding time/frequency resolution and aliasing due to critical sampling), PS employs a dedicated additional complex-valued filterbank with high time resolution and reduced aliasing due to oversampling by factor two. * For each of the binaural _inter-aural cues_ (ILD, ITD, ICC) described previously, corresponding _inter-channel cues_ (IID, IPD and OPD, ICC) are extracted from the original channels by perceptual cue extractors, transmitted as compact side information, and re-synthesized in the PS decoder. * While _Inter-channel Intensity Difference_ (IID) corresponds to the well-known ILD cue and is conceptually similar to the function of the intensity stereo algorithm, two new cue types were introduced in this scheme. As a more practical implementation of ITDs, _Inter-channel Phase Difference_ (IPD) cues plus overall (broadband) phase information (OPD) are provided to model time differences of arrival for laterally placed sound sources. The major innovation, however, lies in the introduction of _Inter-channel Cross Correlation_ (ICC) cues that are vital for representing ambient (decorrelated) sound components, as they are required for proper spatial reproduction of spatially distributed sound sources, e.g., orchestral music or reverberant spaces.