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ss07_hwk2 - E.M.P Sqol H.M M.U Hmer/nia SHMATA kai...

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E.M.P., Sqol  H.M. M.U. SHMATA kai SUSTHMATA Akad.Etoc 2006-2007 Hmer/nia: 04-07-2007 2o SÔnolo Ask sewn Paradotèo: 27-08-2007 'Askhsh 2.1 : Gia ta s mata suneqoÔc qrìnou x ( t ) upologÐste ton Met/smì Fourier : ( a ) x ( t ) = [ te - 2 t sin4 t ] u ( t ) ( b ) x ( t ) = ( 1 - t 2 , 0 < t < 1 0 , alloÔ AntÐstoiqa, upologÐste ta s mata x ( t ) apì touc antÐstoiqouc Fourier Met/smoÔc touc X ( ω ) : ( c ) X ( ω ) = 2sin[3( ω - 2 π )] ( ω - 2 π ) ( d ) | X ( ω ) | = ( | ω | , | ω | ≤ 1 0 , alloÔ kai 6 X ( ω ) = - 3 ω 'Askhsh 2.2 : 'Ena grammikì, qronikˆ ametˆblhto (GQA), aitiatì kai eustajèc sÔsthma S èqei apìkrish suqnìthtac H ( ω ) : H ( ω ) = + 4 6 - ω 2 + 5 ( a ) UpologÐste mia diaforik  exÐswsh pou na sundèei thn eÐsodo x ( t ) kai èxodo y ( t ) tou sust matoc S , ( b ) UpologÐste thn kroustik  apìkrish h ( t ) tou sust matoc S , ( c ) UpologÐste thn èxodo tou sust matoc S ìtan h eÐsodìc tou eÐnai: x ( t ) = e - 4 t u ( t ) - te - 4 t
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