2h_seira - E.M.P., Sqol H.M. & M.U. HmeromhnÐa:...

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Unformatted text preview: E.M.P., Sqol H.M. & M.U. HmeromhnÐa: 22-4-2005 S mata kai Sust mata 2o SÔnolo Ask sewn Akad.Etoc 2004-05 Paradotèo: 11-5-2005 Askhsh 2.1: JewreÐste èna grammikì qronikˆ analloÐwto sÔsthma suneqoÔc qrìnou me kroustik apìkrish h(t) = e−4|t| (1) BreÐte thn anaparˆstash thc exìdou tou mèsw seir¸n Fourier gia tic akìloujec eisìdouc: n (a) x(t) = ∞ n=−∞ (−1) δ(t − n) (b) x(t) ìpwc sto parakˆtw sq ma: Askhsh 2.2: UpologÐste ton metasqhmatismì Fourier gia ta akìlouja s mata: (a) e−3|t| sin 2t 1 + cos πt, |t| ≤ 1 (b) x(t) = 0, |t| > 1 (c) x(t) ìpwc sto parakˆtw sq ma: Askhsh 2.3: KajorÐste to s ma suneqoÔc qrìnou pou antistoiqeÐ stouc parakˆtw meta- sqhmatismoÔc Fourier : (a) X(jω) = 2 sin[3(ω−2π)] (ω−2π) (b) X(jω) = cos(4ω + π/3). (c) X(jω) ìpwc sto parakˆtw sq ma: Askhsh 2.4: Apì to je¸rhma deigmatolhyÐac gnwrÐzoume ìti èna s ma x(t) prèpei na deigmatolhpteÐtai me ènan rujmì megalÔtero apì to eÔroc z¸nhc tou, h isodÔnama me ènan rujmì deigmatolhyÐac megalÔtero apì to diplˆsio thc uyhlìterhc suqnìthtˆc tou. Autì shmaÐnei ìti an to x(t) èqei èna fˆsma ìpwc autì tou sq matoc (a), prèpei na deigmatolhpteÐtai me ènan rujmì megalÔtero apì 2ω2 . Kaj¸c ìmwc to s ma èqei thn enèrgeiˆ tou sugkentrwmènh se mÐa sten z¸nh, ja tan logikì na perimènoume ìti ènac rujmìc deigmatolhyÐac qamhlìteroc apì dÔo forèc thn uyhlìterh suqnìthtˆ tou ja mporoÔse na qrhsimopoihjeÐ. Gia na exetˆsete th dunatìthta thc deigmatolhyÐac enìc zwnoperatoÔ s matoc me ènan rujmì mikrìtero apì to sunolikì eÔroc z¸nhc, jewreÐste to sÔsthma tou sq matoc (b). Jewr¸ntac ìti ω1 > ω2 − ω1 , breÐte thn mègisth tim tou T kai tic timèc twn stajer¸n A, ωa kai ωb ¸ste xr (t) = x(t). Λύσεις 2ης Σειράς Ασκήσεων Σηµάτων Ακαδηµαϊκό έτος 2005-2006 ...
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This note was uploaded on 10/02/2009 for the course G 001 taught by Professor Shmmygr during the Spring '07 term at National Technical University of Athens, Athens.

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