Derivation of Positive Realness Constraint with Specified Maximum Pole Radius and its Application to Design of Low-pass Digital Differentiators

Irie, Hitoshi; Nakamoto, Masayoshi; Yamamoto, Toru

doi:10.1541/ieejeiss.136.123

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…If we substitute Equations and into Equation and expand, we can express a and b in quadratic form as follows:

J false(bold-italica, bold-italicb false) = a^{T} Pa + 2 a^{T} Qb + b^{T} Rb bold-italic .

Here, the P , Q , and R elements become

P_{k, k^{'}} = \{\begin{matrix} left \frac{W_{d} ω_{d}^{3}}{3 π^{2}}, & left if k - k^{'} = 0 \\ left {\bar{P}}_{k, k^{'}}, & left if k - k^{'} \neq 0 \end{matrix},

wherein

\begin{matrix} true \\ right {\overset{P}{true}}_{k, k^{'}} & = & left \frac{W_{d}}{π^{2}} true{\frac{ω_{d}^{2} prefixsin [false(k - k^{'} false) ω_{d}]}{k - k^{'}} + \frac{2 ω_{d} prefixcos [false(k - k^{'} false) ω_{d}]}{{(k - k^{'})}^{2}} \\ left - \frac{2 prefixsin false[(k - k^{'}) ω_{d} false]}{{(k - k^{'})}^{3}} true}, \end{matrix}

\begin{matrix} true \\ right Q_{k, l} & = & left \end{matrix}

…”

Section: Iir Digital Differentiatormentioning

confidence: 99%

“…If we substitute Equations (9) and (13) into Equation (12) and expand, we can express a and b in quadratic form as follows 12 :…”

Section: Cost Functionmentioning

confidence: 99%

“…Figure illustrates a differential operation in the frequency domain. Since the filter demonstrating these characteristics differentiates all the frequency components, it is called a “full‐band differentiator.” In contrast, as illustrated in Figure , studies have also been reported on “low‐pass differentiators” that only differentiate the low‐frequency components . In some applications, low‐pass differentiators are more useful than full‐band differentiators.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, as illustrated in Figure 2, studies have also been reported on "low-pass differentiators" that only differentiate the low-frequency components. [5][6][7][8][9][10][11][12][13][14] In some applications, low-pass differentiators are more useful than full-band differentiators. For example, low-pass differentiators are used in biological signal processing, 5 ultrasonic analysis, 8 and automobile air/fuel ratio sensor diagnosis.…”

Section: Introductionmentioning

confidence: 99%

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Low‐delay and high‐functioning digital differentiators in the big data era

Yoshida

Nakamoto

Aikawa

2018

Elect Comm in Japan

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Since the big data signal has large amount of data, low‐delay signal processing algorithm is required. Digital differentiators are a type of digital signal processing tool, and are useful to estimate the velocity from the position or obtain the image outline. In this article, we introduce finite impulse response (FIR) and infinite impulse response (IIR) digital differentiators. The differentiators can achieve a low‐delay and high‐functioning processing such as low‐pass differentiation.

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“…If we substitute Equations and into Equation and expand, we can express a and b in quadratic form as follows: