# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 1 Introduction  
Psychoacoustic models of human auditory perception have found an important application in the realm of perceptual audio coding, where exploiting limitations of perception and reduction of irrelevance are key to achieving a significant reduction in bitrate while preserving subjective audio quality, even at very high data compression factors. Popular audio codecs, such as Moving Picture Experts Group (MPEG) Advanced Audio Coding (AAC) \"MPEG-2/4 AAC\" [1,2], deliver high quality stereo at bitrates of 96 kbit/s, which corresponds to a data reduction factor of about 15 as compared to a Compact Disc (CD) audio originally sampled at 44.1 kHz and 16 bits. Newer codecs (e.g., High Efficiency AAC v2 [3], Unified Speech and Audio Coding (USAC) [4], or Enhanced Voice Services (EVS) [5]) deliver even higher compression at comparable audio quality. It is intriguing to acknowledge that audio coding exclusively based on reduction of redundancy (i.e., lossless audio coding) would lead to an average data reduction of just about 2:1 for a wide range of CD quality audio material [6]. Thus, the major part of data reduction provided by perceptual audio codecs can be attributed to the extensive exploitation of the properties of perception (irrelevance reduction), for which psychoacoustic models of human auditory perception are key. In general, the most popular approach to perceptual audio encoding can be described as follows (see Figure 1):  
* The time domain audio signal is transformed into a subsampled spectral representation using an analysis filterbank (or equivalently, a transform). This filterbank is usually critically sampled (i.e., the number of output samples is equal to the number of input samples) and (at least nearly) perfectly reconstructed. * A psychoacoustic (perceptual) model is used to analyze the input audio signal and determine relevant perceptual signal aspects, most notably the signal's masking ability (e.g., maskingthreshold) as a function of frequency and time. The result is passed to the quantization and encoding stage to control the injected coding distortion in a way that aims at rendering it inaudible, or at least produce minimal audible distortion and annoyance. This concept of perceptually controlled quantization makes the encoder a _perceptual_ audio encoder;
* The spectral samples are subsequently quantized and possibly _entropy coded_ to reduce the information to a compact representation [7], and packed into a bitstream as binary values;
* In the decoder, the bitstream is unpacked, entropy coding is undone, and the quantized spectral values are mapped back to their original dynamic range and transferred back to a time domain output signal by the synthesis filterbank, i.e., a filterbank that behaves complementarily to the analysis filterbank that has been used by the encoder. The central idea of a perceptual audio codec is to use psychoacoustic criteria, such as masking thresholds, for the quantization of the spectral coefficients in order to maximize _audio quality as perceived by human listeners_ rather than other simple least-mean-square type error metrics metrics such as Signal-to-Noise-Ratio (SNR), Root-Mean-Square (RMS) error, and the like. Specifically, the approach of perceptual audio coding may in fact even imply generating a perceptually shaped spectral distortion profile that provides improved subjective audio quality _at the expense of the signal's global SNR_, as compared to a coder that does not employ psychoacoustic knowledge. More about subjective quality assessment and possible degradation of subjective audio quality can be found in BS.1116 [8], Multi-Stimulus Test with Hidden Reference and Anchor (MUSHRA) [9], and \"What to listen for\" [10]. In order to serve as a part of a perceptual audio coding system, psychoacoustic models do not need to be perfect to satisfy their purpose, and in fact the commonly employed models only represent a small subset of the known properties and abilities of the human auditory system (HAS).