Journal ArticleDOI
On the statistics of fixed-point roundoff error
C. Barnes,Boi Tran,Shu Leung +2 more
TLDR
A statistical analysis of fixed-point round off error is presented that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these conditions are not satisfied.Abstract:
Roundoff error after fixed-point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal. This paper presents a statistical analysis of fixed-point roundoff error that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these conditions are not satisfied. The results show that if the multiplier coefficient is expressed as a = N/M, where M is a positive integral power of two and N is an odd integer, then the errors generated by roundoff after multiplication can generally be modeled as uniformly distributed, white, and uncorrelated with the signal, if the signal has sufficiently wide bandwidth and has a dynamic range that extends over approximately M quantum steps. For narrow-band low-level signals, the roundoff error statistics can differ significantly from the uniform, white, uncorrelated model. In addition, these results show that statistical behavior of roundoff error can differ significantly from that of the quantization error that is generated when a continuous random variable is quantized.read more
Citations
More filters
Journal ArticleDOI
Quantization
Robert M. Gray,David L. Neuhoff +1 more
TL;DR: The key to a successful quantization is the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.
Journal ArticleDOI
Quantization noise spectra
TL;DR: Exact formulas for quantizer noise spectra are developed and several results describing the behavior of quantization noise in a unified and simplified manner are discussed.
Journal ArticleDOI
Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks
P.P. Vaidyanathan,P.-Q. Hoang +1 more
TL;DR: A lattice structure and an algorithm are presented for the design of two-channel QMF (quadrature mirror filter) banks, satisfying a sufficient condition for perfect reconstruction.
Journal ArticleDOI
Implementation of digital controllers—a survey
TL;DR: This paper reviews the issues of digital control implementation, from algorithms through current hardware up to the various problems arising with non-ideal behaviour of digital controllers.
Journal ArticleDOI
Delta operator realizations of direct-form IIR filters
TL;DR: Of all the direct-form structures, the direct form II transposed (DFIIt) delta structure has the lowest quantization noise level at its output, and outperforms both the conventional direct- form (delay) structures, as well as the state-space structures for narrow-band low-pass filters with respect to output roundoff noise.
References
More filters
Journal ArticleDOI
Spectra of quantized signals
TL;DR: Quantizing of time, or time division, has found application as a means of multiplexing telephone channels and the more familiar word “sampling” will be used here interchangeably with the rather formidable term “quantization of time”.
Journal ArticleDOI
A necessary and sufficient condition for quantization errors to be uniform and white
A. Sripad,D. Snyder +1 more
TL;DR: A necessary and sufficient condition is given to model the output of a quantizer as an infinite-precision input and an additive, uniform, white noise.
Journal ArticleDOI
On the interaction of roundoff noise and dynamic range in digital filters
TL;DR: The concept of “transpose configurations” is introduced and is found to be quite useful in digital-filter synthesis; for although such configurations have identical transfer functions, their roundoff-noise outputs and dynamic-range limitations can be quite different, in general.
Journal ArticleDOI
Statistical analysis of amplitude-quantized sampled-data systems
TL;DR: In this article, the authors present a means of evaluating quantitatively the distortion resulting from rough quantization, i.e., rounding errors with values between ± 1/2 and ± 3/2 units.
Journal ArticleDOI
Correlated noise due to roundoff in fixed point digital filters
S. Parker,P. Girard +1 more
TL;DR: In this article, it was shown that correlation between quantization error sources in finite precision fixed point digital filters can be significant even when a filter is driven by a random input, and that correlation coefficients can be estimated in terms of relative values of multiplying constants and the filter structure.