Browsing by Author "Hsu, Han-Wen"

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Autoregressive Modeling of Temporal/Spectral Envelopes With Finite-Length Discrete Trigonometric Transforms
(2010-07-01)
Hsu, Han-Wen
;
Liu, Chi-Min
;
資訊工程學系
;
Department of Computer Science
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).
Decimation-Whitening Filter in Spectral Band Replication
(2011-11-01)
Hsu, Han-Wen
;
Liu, Chi-Min
;
資訊工程學系
;
Department of Computer Science
MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) has adopted spectral band replication (SBR) to efficiently compress the high-frequency part of the audio. In SBR, linear prediction is applied to low-frequency subbands to suppress tonal components and smooth the associated spectra for replicating to high-frequency bands. Such a tone-suppressing process is referred to as whitening filtering. In SBR, to avoid the alias artifact incurred by spectral adjustment, a complex filterbank instead of real filterbank is adopted. For QMF subbands, this paper demonstrates that the linear prediction defined in the SBR standard results in a predictive bias. A new whitening filter, called the decimation-whitening filter, is proposed to eliminate the predictive bias and provide advantages in terms of noise-to-signal ratio measure, frequency resolution, energy leakage, and computational complexity for SBR.
Fast Radix-q and Mixed-Radix Algorithms for Type-IV DCT
(2008)
Hsu, Han-Wen
;
Liu, Chi-Min
;
資訊工程學系
;
Department of Computer Science
This letter proposes a fast radix-q algorithm to compute type-IV discrete cosine transform (DCT) of the length q(lambda), where q is an odd positive integer. The proposed fast radix-q algorithm has merits in computational complexity, parallelism, and numerical stability over existing algorithms. Furthermore, the fast radix-q algorithm is used to develop the fast mixed-radix type-II/type-IV DCT algorithm for composite lengths.
High frequency reconstruction by linear extrapolation
(2008-05-08)
Liu, Chi-min
;
Lee, Wen-chieh
;
Hsu, Han-Wen
High frequency components of audio signals are reconstructed from the aspects of envelope and fine detail. The envelopes of the high frequency components are found through linear extrapolation of signals with frequencies lower than a cutoff frequency point. One method of reconstructing high frequency components is based on the linear extrapolation on the logarithm scale magnitudes of the transform coefficients of the audio signal in a frequency domain. The linear extrapolation is a linear approximation based on minimizing least squares of the logarithm scale magnitudes of the transform coefficients of the low frequency components. Another method is based on the linear extrapolation on the logarithm scale magnitudes of the envelope elements of the filterbank signals of the audio signal over a time segment. The linear extrapolation is a linear approximation based on minimizing least squares of the logarithm scale magnitudes of the envelope elements of the low frequency filterbank signals.