Title :
Conditions for optimality of scalar feedback quantization
Author :
Derpich, Milan S. ; Quevedo, Daniel E. ; Goodwin, Graham C.
Author_Institution :
Sch. of Electr. Eng. & Comput. Sci., Newcastle Univ., Newcastle, NSW
fDate :
March 31 2008-April 4 2008
Abstract :
This paper presents novel results on scalar feedback quantization (SFQ) with uniform quantizers. We focus on general SFQ configurations where reconstruction is via a linear combination of frame vectors. Using a deterministic approach, we derive two necessary and sufficient conditions for SFQ to be optimal, i.e., to produce, for every input, a quantized sequence that is a global minimizer of the 2-norm of the reconstruction error. The first optimality condition is related to the design of the feedback quantizer, and can always be achieved. The second condition depends only on the reconstruction vectors, and is given explicitly in terms of the Gram matrix of the reconstruction frame. As a by-product, we also show that the the first condition alone characterizes scalar feedback quantizers that yield the smallest MSE, when one models quantization noise as uncorrelated, identically distributed random variables.
Keywords :
matrix algebra; quantisation (signal); signal reconstruction; Gram matrix; frame vectors; identically distributed random variables; quantized sequence; reconstruction error; scalar feedback quantization; uniform quantizers; Australia; Computer science; Delta-sigma modulation; Digital signal processing; Feedback; Quantization; Random variables; Signal processing; Sufficient conditions; Vectors; Frames; Quantization; Sigma-Delta Modulation;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on
Conference_Location :
Las Vegas, NV
Print_ISBN :
978-1-4244-1483-3
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2008.4518468