General moments of roundoff error

Abstract Li and Nadarajah [Signal Processing 127 (2016) 185–190] derived expressions for mean and variance of roundoff error for any continuous random variable. Here, we derive expressions for general moments of the roundoff error, allowing one to study other aspects of roundoff error than just mean and variance. The expressions are specialized for 10 commonly used distributions in signal processing. Numerical studies checking the correctness of the derived expressions are given.

[1]  B. Liu,et al.  ROUND-OFF ERROR OF FLOATING-POINT DIGITAL FILTERS, , 1968 .

[2]  T. Murakami,et al.  An optimization procedure to minimize the roundoff noise in cascade floating-point digital filters , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[3]  Bernard Widrow,et al.  Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications , 2008 .

[4]  Shu Hung Leung,et al.  On the statistics of fixed-point roundoff error , 1985, IEEE Trans. Acoust. Speech Signal Process..

[5]  Jianhua Ge,et al.  Trapezoidal companding scheme for peak-to-average power ratio reduction of OFDM signals , 2009 .

[6]  P. W. Wong Quantization noise, fixed-point multiplicative roundoff noise, and dithering , 1990, IEEE Trans. Acoust. Speech Signal Process..

[7]  S. H. Ardalan,et al.  Fixed-point roundoff error analysis of the exponentially windowed RLS algorithm for time-varying systems , 1987, IEEE Trans. Acoust. Speech Signal Process..

[8]  Mit Press Round-Off Error of Floating-Point Digital Filters , 1969 .

[9]  I. Kollar,et al.  Digital dither: decreasing round-off errors in digital signal processing , 2003, IEEE International Symposium on Intelligent Signal Processing, 2003.

[10]  Xiaojun Liu,et al.  On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1 , 2008 .

[11]  Igor G. Vladimirov,et al.  A Uniform White-Noise Model for Fixed-Point Roundoff Errors in Digital Systems , 2002 .

[12]  Yuri A. Gadzhiev,et al.  On the variance of a centered random value roundoff error , 2015, Signal Process..

[13]  Saralees Nadarajah,et al.  Mean and variance of round off error , 2016, Signal Process..

[14]  Yong Ching Lim,et al.  Roundoff Noise Analysis of Signals Represented Using Signed Power-of-Two Terms , 2007, IEEE Transactions on Signal Processing.