1 Erratum to: Med Biol Eng Comput DOI 10.1007/s11517-012-0954-0

Due to an equations formatting error, the presentation of some expressions was incorrect. A list of these expressions is given below:

  • Sect. 2.3, ninth paragraph: \(d_{\rm s}^{\rm P}(n)\) should be read as \(d_{\rm BRV}^{u}(n). \)

  • Sect. 3.1, second paragraph: \(d_{\rm s}^{\rm P}(n)\) should be read as \(d_{\rm PWV}^{u}(n). \)

  • Table 2: The correct table is given at the end of this erratum.

    Table 2 Percentage of utilization of each DR signal in combination of PRV, PAV and PWV
    Full size table

  • Sect. 2.4, third paragraph: \(f^{\rm P}_{\rm s}(j, k)\) should be read as \(f^{\rm I}_{\rm P}(j, k). \)

  • Sect. 2.4, fifth and sixth paragraphs: The corrected paragraphs are given below.

In the averaged spectrum \(\bar{S}_{k}(f)\) the algorithm also searches the largest peak [denoted \(f_p^{{\rm I}_a}(k)\)] and \(f_p^{{\rm II}_a}(k)\) defined as the nearest to \(f_{\rm R}(k-1)\) inside the interval \(\Upomega_{\rm R}(k)\) which is at least larger than 85 % of \(f_p^{{\rm I}_a}(k). \) At this time the reference frequency \(f_{\rm R}(k)\) can be updated as:

$$f_{\rm R}(k) = \beta f_{\rm R}(k-1) + (1-\beta) f_{p}(k) $$
(21)

where β denotes the forgetting factor and f p (k) is defined by

$$f_p(k)= \left\{ \begin{array}{ll} f_p^{{\rm II}_{a}}(k),& \exists f_p^{{\rm II}_{a}}(k) \\ f_p^{{\rm I}_{a}}(k), & \hbox{otherwise} \end{array} \right. . $$
(22)

Finally, estimated respiration rate \(\hat{f}(k)\) is defined as:

$$ \hat{f}(k) = \alpha \hat{f}(k-1) +(1-\alpha) f_p(k) $$
(23)
$$ \alpha= \left\{ \begin{array}{ll} \alpha_2, &\exists f_p^{{\rm II}_a}(k) \\ \alpha_1, & \hbox{otherwise} \end{array} \right. $$
(24)

where α2 ≤ α1, providing more memory when \(f^{{\rm II}_{a}}_p(k)\) could not be set.