# Psychaocoustic Models for Perceptual Audio Coding--A Tutorial Review
## 4 Models for Parametric Audio Coding
### Parametric (monophonic) Waveform Coding  
An early example of the integration of a parametric coding tool into the classic filterbank-based perceptual audio coder is _Perceptual Noise Substitution_ (PNS) [17; 55]. A similar concept is found under the name _Noise Filling_[18]. The underlying idea of the tool is based on the psychoacoustic observation that individual realizations and observations of noise-like signals cannot be distinguished perceptually from each other if their spectral or temporal envelopes are similar enough, i.e., that the actual signal waveform does not play a relevant role within the HAS. Consequently, spectral parts of the input signal that were identified as being noise-like are omitted from regular transmission of spectral coefficients. Instead, the energy levels present in the noisy frequency bands are transmitted as parametric side information to the decoder and a pseudo-random noise generator re-inserts spectral coefficients with appropriate scaling into the respective frequency bands. A perceptual model for controlling PNS processing within a codec may include the following aspects:  
* First, the model has to detect which frequency bands solely contain noise-like signal components (signals without a distinct spectral fine structure). This task is related to a tonality calculation, as it is needed for masking calculations, but may employ different tonality or noisiness measures. This ensures that no signal parts containing tonal components are substituted erroneously by noise in the decoder. * Furthermore, the model should also detect if the noise signal in a particular detected coder frequency band has any relevant or distinct temporal fine structure that could not be reproduced appropriately by pseudo-random noise. As one example, the temporally modulated noise of applause signals also includes transients, and thus cannot be substituted by PNS without causing significant artifacts. While PNS allows for parametric coding of noise-like components in the high-frequency (HF) region, the much more successful _bandwidth extension (BWE)_ techniques allow for parametric substitution of the entire high-frequency range of an audio signal without severe restrictions. The first widely deployed BWE technique is called _Spectral Bandwidth Replication (SBR)_[17; 56]. The basic idea is that above a certain border frequency (e.g., 6 kHz), the HF part of the signal spectrum is entirely reconstructed from the transmitted low-frequency (LF) part. The LF part is transposed (i.e., linearly shifted in frequency) to higher frequencies and adapted in its time/frequency properties to match the perceptual properties of the original HF part as closely as possible using a compact set of perceptually motivated parameters. Strictly speaking, SBR and related techniques are _hybrid approaches_ between parametric and waveform coding, since the waveform transmitted for the LF part is subsequently transformed into the HF part by parametric means. This is sometimes denoted as being a semi-parametric processing. The perceptual control of SBR in the decoder typically performs the following steps:  
* The spectral envelope of the original HF part is captured with appropriate time/frequency resolution and sent as compact parameters to the decoder as side information. * The properties of the transposed LF frequency content are compared to the properties of the original HF part. When significant differences arise, additional post-processing of the transposed part has to be enabled:
* When the target timbre characteristic is much more tonal than the one of the transposed LF part, additional sine tones can be generated for each band [57]. * When the target timbre characteristic is noise-like, whereas the transposed source LF region is tonal (which is common for music signals), the transposed signal spectrum can be flattened or whitened to a selectable extent.