Ideally low-pass filter is a stable system?

Any of the textbooks with the system has such a conclusion: The charging condition of the LTI system stability is: unit impulse response h (t) / h (n) absolute can be absolute / absolute. But what about the ideal low pass filter? Is it a stable system? If so, is its unit impunity to meet absolute volume? If not, you can find a boundary input, is it unbounded by an ideal low pass? Below is an old text of Teacher Tang Jun, Xiamen Institute of Technology, this confusion has been unsolved, welcome everyone to discuss. The following papers are extracted from the "Signal and System Learning Guidance": The reference answer given by the question of the question is B, that is, the ideal low pass filter is stable, this seems to have no doubt? ! The second edition of the "Signal and System" second edition Auburnheim Liu Shusang translation (6.19) The formula is not absolute, and about this, refer to "Digital Signal Process theory, Algorithm and Implement" Second Edition Hu Guangshu P96, extracted as follows: In summary, you can get the following two conclusions: 1. The low pass filter is stable; 2, its unit impulse response H (t) is a square, but is not absolute. However, there is a conclusion in almost all signals and systems of the system: The charging condition of the LTI system is: the unit impulse response absolute or unit pulse response is absolutely possible. The second edition of the "Signal and System" second edition is taken from the "Signal and System" second edition. The fourth edition of the "Signal and Systematic System Analysis" is taken from Wu Da Zheng P339: Through the above analysis, should the LTI system stability condition should be modified? Is it wrong in the analysis process? The above is the original text of Teacher Tang. I have reviewed the books of digital signal processing, and there is the same conclusion for discrete time systems. The following is a P30 page of Tsinghua University Press to Cheng Peiqing "Digital Signal Processing" Tsinghua University Press. Below is the book in P96 and P97, which expounds the absolute and square cocoa, and it is clear that the ideal low-pass filter unit impulse H (n) is not satisfied with absolute and satisfying square. However, its stability was not analyzed in the book. So, is the ideal low-pass filter, is it a stable system? Welcome everyone to discuss. , Read the full article, original title: a question about the stability of the LTI system Article Source: [Micro Signal: Signalandsystem_DSP, WeChat public number: Digital Signal Processing Counseling] Welcome to add attention! Please indicate the source of the article.

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