NDLI: Covariance calculation for floating-point state-space realizations

Content Provider	IEEE Xplore Digital Library
Author	Sangho Ko Bitmead, R.R.
Copyright Year	1991
Abstract	This paper provides a new method for analyzing floating-point roundoff error for digital filters by using "finite signal-to-noise" models whose noise sources have variances proportional to the variance or power of the corrupted signals. With this model, a new expression for output error covariance of floating-point arithmetic is derived the in case of double or extended precision accumulation. The output error covariance shows that the optimal state space realization for floating point is the same as that of the fixed-point case, except for two cases: when the filter has poles extremely close to the unit circle or when final quantization to precisions shorter than single precision is employed. An explicit formula is found for determining the minimum number of mantissa bits for stable realization.
Sponsorship	IEEE Signal Processing Society
Starting Page	3370
Ending Page	3377
Page Count	8
File Size	334699
File Format	PDF
ISSN	1053587X
Volume Number	52
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Roundoff errors State-space methods Additive white noise Error analysis Signal analysis Floating-point arithmetic Fixed-point arithmetic Equations Linear systems Analysis of variance roundoff noises Covariance multiplicative white noises optimal state space realizations
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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