Wiley signals and systems e book TLFe BO 402

16.1 BIBO, Iiiipulse Response arid El'fequency Kc>sponst:Curve 387 The slim itself is a known harmonic series, arid does riot oo~iverge,which tihows that the impulse response of the ideal low-pass cannot bc absolutely integrated The ided hW-J2aSS is therefore neithel c i ~ u s dnor stable Q Af'ter this rxample we have to ask whether it is worth examining such idralised systcms, when they arc innpossible to impleiiirnt, The answer is typical from tlic point of vicw of' systems theory: o The ideal low-pass filter with an entiiely real rectaiigular frqiency plot i s a very simple cority)t It allows many operations to be coiisideied in tire simplest form, for example, limiting spectra, and reconstructing contiriirour sigiials fruiii samplPs The ideal lotv-pass rmriot be prrciscly rediwd lmt can bc apprtmimateil if miiie coritaehsions can be accepted A n cxarnple for this coiild be: - Noncritical sampliiig Oversampling allows the steepn of thc edges to be rcduced (see Figure 11.13).'rhe irripiilsc rqmrrse eii drcays more quickly and therefore can hc absolutely integrated and stable behaviour has beeii achieved - Permitting a time-delay filtcr can be tipproximated Ttic impulse resporise of' the ideal lowwell by i i causal system if it is shifted far eiiough to t h c righl