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A#02 - Assignment#02 p.1 ECSE-2410 Signals Systems Spring...

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Assignment #02 – p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 01/20/09 1(40). Evaluate: (a) (b) (c) (d) . τ τ δ τ d e t ) 1 ( τ τ τ d u e t ) ( τ τ δ τ d e ) 2 ( + τ τ τ τ d u u e ) 1 ( ) ( - 2(30). Given signal 2 1 x ( t ) 1 t -1 0 (a) Express ( ) t x in terms of step and ramp functions. (b) find the equation for the derivative, ( ) ( ) dt t dx t w . = (c) Sketch ( ) t w 3(20). Using the basic definitions of linearity and/or time-invariance, verify that (a) system ( ) ( ) 1 2 = t x t t y is linear. x ( t ) y ( t ) System (b) system is time-invariant. ( ) ( ) 2 2 = t x t y 4(20). The output of the LTI system is ( ) t y , when the input is ( ) t x , as shown. 0 1 2 y ( t ) t 1 2 3 x ( t ) t 1 0 1 LTI Use superposition to graph the output of this system when the input is 0 1 2 x ( t ) t 1
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