# A#08 - Assignment#8 ~— 11.1 ECSE-24IO Signals& Systems...

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Unformatted text preview: Assignment #8 ~— 11.1 ECSE-24IO Signals & Systems — Spring 2007 Due: Fri 02/16/07 W WWWWM 1. (30 points) The signal :66) described by {I 43:31 X09 2 0 else 2 sin a: has the transformX (60) m m 2 sinc (co) . a) (a) (5) Plot the magnitude of X (co) . For the signais below, ﬁnd their Fourier transforms. 1, ~ 0.1 < t < 0.1 (b) (5) xb (t) m 1 , Plot the magnitude of X ,3 (co) . Use the same scaie as par? (3). 0, e se 1, — 10 <1 <10 (C) (5) 36¢ (0 m 1 3 P10! the magnitude of Xe (co). Use the same scale as parts (a) and (b). 0, e se (d), (3) Which signal contains the widest range of frequencies? (2) Which signal contains the narrowest range of frequencies? 1, 0<t<2 (agenda): 2, 2<z<3. Find Xd(co). O, eise 2. (20). The signal beiow is deﬁned over the interval —3 E I g 3. (a) (i 5) Find the Fourier transfomi for this sigma}. Use properties and know transforms (Tables 4.1 and 42 in the text) ofhasic signeis. No credit for direct integration of the deﬁning formula (equation 4.9). Use sine functions Wherever possible. (19) {5) P10: ﬂie magnitude of X(a)) . Assignment #8 w p.2 ECSE-2410 Signals & Systems ~ Spring 2007 Due: Fri 02/16/07 3.(35) An aperiodic signal has the following Fourier transform, 1 _ 8—1702 j a) a.) (5) Find the | X (wﬂend express in terms of sine functions. X(w): b.) (5) Sketch the [X(a))[. 1_2e-jwz+ejmg Repearparts (a) (10 pts) and (b) (5 pts) for X 2 (w) r M. j a) c.) (10) Find x2 (1:) . the inverse transform of X 2 (co) . 4415) a.) (10) Find the Fourier transform of I, 0 <1? < 1 x09 : 2-r,1<r<2 0, else b.) (5) Express! X (60)] in terms of sine functions. ...
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