The Role of GTD in Optimizing Perfect Reconstruction Filter Banks

Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) filter banks as a subband coder for optimizing the theoretical coding gain. We foc...

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Vydané v:IEEE transactions on signal processing Ročník 60; číslo 1; s. 112 - 128
Hlavní autori: Ching-Chih Weng, Vaidyanathan, P. P.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY IEEE 01.01.2012
Institute of Electrical and Electronics Engineers
Predmet:
Applied sciences
Bit rate
Coding, codes
Decorrelation
Detection, estimation, filtering, equalization, prediction
Encoding
Exact sciences and technology
Filter banks
Frequency dependence
generalized triangular decomposition
Information, signal and communications theory
linear prediction
Loading
Matrix decomposition
Noise
Signal and communications theory
Signal, noise
subband coders
Telecommunications and information theory
transceivers
Performance evaluation
Frequency dependence
Input signal
Wireless telecommunication
Filter banks
Decision feedback equalizers
Optimization
Coding
transceivers
Traffic control
Filter bank
Decorrelation
Pretreatment
generalized triangular decomposition
Subband decomposition
Optimal filter
Coding circuit
Flow rate regulation
Power spectral density
Teletraffic
Equalization
Information transmission
Optimal solution
Telecommunication system
Signal processing
Numerical simulation
Geometrical theory of diffraction
subband coders
linear prediction
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí:Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) filter banks as a subband coder for optimizing the theoretical coding gain. We focus on perfect reconstruction orthonormal GTD filter banks and biorthogonal GTD filter banks. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can, with no loss of optimality, be used in the optimal biorthogonal GTD coders, which solves the granularity problem in the conventional optimum bit loading formula. We then extend the use of GTD filter banks to wireless communication systems, where linear precoding and zero-forcing decision feedback equalization is used in frequency selective channels. We consider the quality of service (QoS) problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints. Optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent GTD of the channel frequency response.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2169252