標題: Autoregressive Modeling of Temporal/Spectral Envelopes With Finite-Length Discrete Trigonometric Transforms 作者: Hsu, Han-WenLiu, Chi-Min資訊工程學系Department of Computer Science 關鍵字: Autoregressive (AR) modeling;discrete cosine transform (DCT);discrete trigonometric transform (DTT);generalized discrete Fourier transform (GDFT);Hilbert envelope;linear prediction;frequency-domain linear prediction;linear prediction in spectral domain;temporal noise shaping (TNS) 公開日期: 1-七月-2010 摘要: The theory of autoregressive (AR) modeling, also known as linear prediction, has been established by the Fourier analysis of infinite discrete-time sequences or continuous-time signals. Nevertheless, for various finite-length discrete trigonometric transforms (DTTs), including the discrete cosine and sine transforms of different types, the theory is not well established. Several DTTs have been used in current audio coding, and the AR modeling method can be applied to reduce coding artifacts or exploit data redundancies. This paper systematically develops the AR modeling fundamentals of temporal and spectral envelopes for the sixteen members of the DTTs. This paper first considers the AR modeling in the generalized discrete Fourier transforms (GDFTs). Then, we derive the modeling to all the DTTs by introducing the analytic transforms which convert the real-valued vectors into complex-valued ones. Through the process, we build the compact matrix representations for the AR modeling of the DTTs in both time domain and DTT domain. These compact forms also illustrate that the AR modeling for the envelopes can be performed through the Hilbert envelope and the power envelope. These compact forms can be used to develop new coding technologies or examine the possible defects in the existing AR modeling methods for DTTs, We apply the forms to analyze the current temporal noise shaping (TNS) tool in MPEG-2/4 advanced audio coding (AAC). URI: http://dx.doi.org/10.1109/TSP.2010.2047105http://hdl.handle.net/11536/5165 ISSN: 1053-587X DOI: 10.1109/TSP.2010.2047105 期刊: IEEE TRANSACTIONS ON SIGNAL PROCESSING Volume: 58 Issue: 7 起始頁: 3692 結束頁: 3705 顯示於類別： 期刊論文