Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Signal Processing with Lapped Transforms
Signal Processing with Lapped Transforms
Fast IMDCT and MDCT algorithms - a matrix approach
IEEE Transactions on Signal Processing
Computing the discrete-time “analytic” signal via FFT
IEEE Transactions on Signal Processing
Double-Talk-Robust Prediction Error Identification Algorithms for Acoustic Echo Cancellation
IEEE Transactions on Signal Processing
Autoregressive Modeling of Temporal Envelopes
IEEE Transactions on Signal Processing
On minimum/maximum/all-pass decompositions in time and frequencydomains
IEEE Transactions on Signal Processing
A Novel Audio Coding Scheme Using Warped Linear Prediction Model and the Discrete Wavelet Transform
IEEE Transactions on Audio, Speech, and Language Processing
Compression Artifacts in Perceptual Audio Coding
IEEE Transactions on Audio, Speech, and Language Processing
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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).