Roundoff error analysis of the discrete Wigner distribution using fixed-point arithmetic

Finite word-length effects in implementation of distributions for time-frequency signal analysis

“…The effects of finite register length have been analyzed in the case of the WD [6], [14]. This correspondence extends the analysis of [6] and [14] to the TFD's from the general CD [5], [8], [19] cases of floating-point and fixed-point representations.…”

“…The effects of finite register length have been analyzed in the case of the WD [6], [14]. This correspondence extends the analysis of [6] and [14] to the TFD's from the general CD [5], [8], [19] cases of floating-point and fixed-point representations. Distributions' variance and the signal-to-quantization noise ratio (SNR) have been derived (using results from [1], [7], and [15]) and used as criteria for quantitative comparison of various TFD's from the CD.…”

“…However, it is possible to cause an overflow when preforming an addition operation. In the analysis of the influence of the finite register length in fixedpoint arithmetic, we will use the model C(n; k; ') = L01 i=0L r(n; i)e 0j ki + (n; i; k) r(n; i) = Quantization errors stemming from this model are analogous to the ones induced by the floating-point arithmetic (Section III) [6], [11], [14] with the corresponding variances 02b =12-basic variance value). However, as opposed to the case of floating-point arithmetic, these errors are additive [11].…”

“…Rounding of arithmetic operation results also introduce errors, whose influence to the final results depends on the chosen number representation (fixed point or floating point). Fixed-point arithmetic is characterized by a narrow range and is more sensitive to addition overflow [6], [11]. To overcome this problem, the floating-point representation and arithmetic is used.…”