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The quantization error of a digital filter employing fixed-point arithmetic with sign-magnitude truncation is analyzed. The effect of coefficient quantization is also included. Exact analyses are presented first for Gaussian, sinusoidal and Gaussian plus sinusoidal inputs. Quasi-linearization is then employed to yield a simple computation method of the output noise variance. The resulting expression contains parameters that depend on the input signal statistics. An upper bound is given that is independent of these statistics. Explicit expressions are given for the second-order sections of the digital filter realized in the D1 and D2 forms together with a general expression for the cascade connection of the second-order sections. 相似文献
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Kotaro Komatsu 《Educational Studies in Mathematics》2017,96(2):129-144
In contrast to existing research that has typically addressed the process from example generation to proof construction, this study aims at enhancing empirical examination after proof construction leading to revision of statements and proofs in secondary school geometry. The term “empirical examination” refers to the use of examples or diagrams to investigate whether a statement is true or a proof is valid. Although empirical examination after proof construction is significant in school mathematics in terms of cultivating students’ critical thinking and achieving authentic mathematical practice, how this activity can be fostered remains unclear. This paper shows the strength of a particular kind of mathematical task, proof problems with diagrams, and teachers’ roles in implementing the tasks, by analysing two classroom-based interventions with students in the eighth and ninth grades. In the interventions, the tasks and the teachers’ actions successfully prompted the students to discover a case rejecting a proof and a case refuting a statement, modify the proof, properly restrict the domain of the statement by disclosing its hidden condition, and invent a more general statement that was true even for the refutation of the original statement. 相似文献
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Kotaro Hashikura Jad Musaddiq Bin Jaafar Akira Kojima Md Abdus Samad Kamal Kou Yamada 《Journal of The Franklin Institute》2021,358(1):474-493
This paper addresses the output regulation problem for a class of preview control systems, and derives a state feedback law which suppresses the steady-state error caused by the excitation from polynomial or sinusoidal exogenous inputs. Recently, the output regulation condition for the broader class of distributed parameter systems is characterized via the operator regulator equation. We show that a solution of the operator regulator equation specialized to the preview control system is obtained by solving the matrix regulator equation, and provide the state feedback law which attenuates the transient error optimally with respect to an LQ (Linear Quadratic) performance index. 相似文献
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