# A Multi-Frame PCA-Based Stereo Audio Coding Method
## 1 Introduction  
The goal of audio coding is to represent audio in digital form with as few bits as possible while maintaining the intelligibility and quality required for particular applications [1]. In audio coding, it is very important to deal with the stereo signal efficiently, which can offer better experiences of using applications like mobile communication and live audio broadcasting. Over these years, a variety of techniques for stereo signal processing have been proposed [2, 3], including M/S stereo, intensity stereo, joint stereo, and parametric stereo. M/S stereo coding transforms the left and right channels into a mid-channel and a side channel. Intensity stereo works on the principle of sound localization [4]: humans have a less keen sense of perceiving the direction of certain audio frequencies. By exploiting this characteristic, intensity stereo coding can reduce the bitrate with little or no perceived change in apparent quality. Therefore, at very low bitrate, this type of coding usually yields a gain in perceived audio quality. Intensity stereo is supported by many audio compression formats such as Advanced Audio Coding (AAC) [5, 6], which is used for the transfer of relatively low bit rate, acceptable-quality audio with modest internet access speed. Encoders with joint stereo such as Moving Picture Experts Group (MPEG) Audio Layer III (MP3) and Ogg Vorbis [7] use different algorithms to determine when to switch and how much space should be allocated to each channel (the quality can suffer if the switching is too frequent or if the side channel does not get enough bits). Based on the principle of human hearing [8, 9], Parametric Stereo (PS) performs sparse coding in the spatial domain. The idea behind parametric stereo coding is to maximize the compression of a stereo signal by transmitting parameters describing the spatial image. For stereo input signals, the compression process basically follows one idea: synthesizing one signalfrom the two input channels and extracting parameters to be encoded and transmitted in order to add spatial cues for synthesized stereo at the receiver's end. The parameter estimation is made in the frequency domain [10; 11]. AAC with Spectral Band Replication (SBR) and parametric stereo is defined as High-Efficiency Advanced Audio Coding version 2 (HE-AACv2). On the basis of several stereo algorithms mentioned above, other improved algorithms have been proposed [12], which causes Max Coherent Rotation (MCR) to enhance the correlation between the left channel and the right channel, and uses MCR angle to substitute the spatial parameters. This kind of method with MCR reduces the bitrate of spatial parameters and increases the performance of some spatial audio coding, but has not been widely used. Audio codec usually uses subspace-based methods such as Discrete Cosine Transform (DCT) [13], Fast Fourier Transform (FFT) [14], and Wavelet Transform [15] to transfer audio signal from time domain to frequency domain in suitably windowed time frames. Modified Discrete Cosine Transform (MDCT) is a lapped transform based on the type-IV Discrete Cosine Transform (DCT-IV), with the additional property of being lapped. Compared to other Fourier-related transforms, it has half as many outputs as inputs, and it has been widely used in audio coding. These transforms are general transformations; therefore, the energy aggregation can be further enhanced through an additional transformation like PCA [16; 17], which is one of the optimal orthogonal transformations based on statistical properties. The orthogonal transformation can be understood as a coordinate one. That is, fewer new bases can be selected to construct a low dimensional space to describe the data in the original high dimensional space by PCA, which means the compressibility is higher. Some work was done on the audio coding method combined with PCA from different views.