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ss04_hwk2 - Ε.Μ.Π Σχολή Η.Μ Μ.Υ Ηµερ/νια...

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Ε . Μ . Π . , Σχολή Η . Μ . & Μ . Υ . Η μ ερ / νια : 30-04-2004 Σή μ ατα και Συστή μ ατα 2 η Σειρά Ασκήσεων Ακαδ . Έτος 2003-04 Παράδοση : 12/05/2004 Άσκηση 2.1 : Να υπολογιστεί η σειρά Fourier της περιοδικής συνάρτησης < < + = 2 t 0 , 8 1 0 2 - , 8 1 ) ( T T t t T T t t x όπου Τ είναι η περίοδος . Άσκηση 2.2 : Να βρεθεί ο Μετασχη μ ατισ μ ός Fourier της συνάρτησης 2 2 2 2 1 ) ( σ π σ t e t x = Τι παρατηρείτε ; Υπόδειξη : Ισχύει ότι a a x ax e a dx e 4 4 ) ( 2 2 γ β γ β π + + = Άσκηση 2.3 : Έστω το ιδανικό βαθυπερατό φίλτρο μ ε απόκριση συχνότητας > < = c c H ω ω ω ω ω , 0 , 1 ) ( Θεωρού μ ε ότι η είσοδος στο φίλτρο είναι το σή μ α x ( t ) = e -2 t u ( t ). Να υπολογισθεί η έξοδος του φίλτρου
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