DocumentCode :
1365093
Title :
Theory and design of dyadic subband tree structures with embedded PDF-optimized quantizers
Author :
Choi, Ginkyu ; Haddad, Richard A.
Author_Institution :
Telecommun. R&D Center, Samsung Electron. Co. Ltd., Seoul, South Korea
Volume :
46
Issue :
5
fYear :
1998
fDate :
5/1/1998 12:00:00 AM
Firstpage :
1260
Lastpage :
1274
Abstract :
We develop a methodology for the analysis of signal quantization effects in critically sampled dyadic subband tree structures using a nonlinear gain-plus-additive-noise model for the probability density function (PDF)-optimized quantizer. We constrain the two-band nonquantized and uncompensated structure at each level to be perfect reconstruction (PR). We develop an equivalent uniform filter bank followed by its polyphase structure described by primitive submatrices and compute a rigorously correct mean squared error (MSE) in the frequency domain using cyclostationary concepts in terms of: (1) the allocated quantizer bits; (2) the filter coefficients; (3) an embedded compensation parameter vector. This MSE is then minimized over all three items above. Our optimization method is applied to the specific case of a four-channel dyadic tree with average bit rate constraint. This tree is represented by an eight-channel polyphase equivalent whose interchannel signals are correlated. We show how to represent rigorously the correlation of random noise between channels due to the embedded quantizers. Our design of paraunitary and biorthogonal structures with identical and nonidentical stages is performed, compared, and validated by computer simulation under the assumption of uncorrelated cross band noise. The nonidentical stage biorthogonal filter bank turned out to have the best performance in MSE sense, but the most robust structure is the nonidentical stage paraunitary filter bank
Keywords :
band-pass filters; compensation; digital filters; frequency-domain synthesis; least mean squares methods; minimisation; quantisation (signal); random noise; signal representation; signal sampling; tree data structures; allocated quantizer bits; average bit rate constraint; biorthogonal structures; critically sampled dyadic subband tree structures; cyclostationary concepts; dyadic subband tree structures; eight-channel polyphase equivalent; embedded PDF-optimized quantizers; embedded compensation parameter vector; embedded quantizers; filter coefficients; four-channel dyadic tree; frequency domain; identical stages; interchannel signals; nonidentical stage biorthogonal filter bank; nonidentical stage paraunitary filter bank; nonidentical stages; nonlinear gain-plus-additive-noise model; paraunitary structures; perfect reconstruction; performance; polyphase structure; primitive submatrices; probability density function; random noise; rigorously correct mean squared error; signal quantization effects; two-band nonquantized uncompensated structure; uncorrelated cross band noise; uniform filter bank; Bit rate; Embedded computing; Error correction; Filter bank; Frequency domain analysis; Optimization methods; Probability density function; Quantization; Signal analysis; Tree data structures;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.668790
Filename :
668790
Link To Document :
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