A Note on BIBO Stability

被引：5
作者：
Unser, Michael [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Biomed Imaging Grp, CH-1015 Lausanne, Switzerland
来源：
IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2020年 / 68卷
基金：
瑞士国家科学基金会;
关键词：
Convolution; Large scale integration; Kernel; Extraterrestrial measurements; Biomedical measurement; Standards; Atmospheric measurements; filters; filtering theory; stability;
D O I：
10.1109/TSP.2020.3025029
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identity operator. The purpose of this note is to clarify the issue while presenting some fixes. In particular, we show that a linear shift-invariant system is BIBO-stable in the L8-sense if and only if its impulse response is included in the space of bounded Radon measures, which is a superset of L1(R) (Lebesgue's space of absolutely integrable functions). As we restrict the scope of this characterization to the convolution operators whose impulse response is a measurable function, we recover the classical statement.
引用
收藏
页码：5904 / 5913
页数：10
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