hw4 - Assignment#4 ECSE-2410 Signals Systems Fall 2005 Tue...

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Assignment #4 ECSE-2410 Signals & Systems - Fall 2005 Tue 09/13/05 1(15). Suppose the step response of a discrete-time, LTI system is < < = n n n n n y step 2 , 3 2 0 , 0 , 0 ] [ . (a) Sketch ] [ n y step . (b) Suppose the input to this system is { } ,... 0 ..., 0 , 1 , 1 , 1 , 1 ] [ 1 = n x . First, express ] [ 1 n x in terms of step functions and then use the linearity and time-invariance properties to express the output, ] [ 1 n y , in terms of ] [ n y , and sketch. (c) Suppose the input is { } ,... 0 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 ] [ 2 - - - - = n x . Express the output, ] [ 2 n y , in terms of ] [ 1 n y , and sketch. 2(20). Suppose the impulse response of a discrete-time, LTI system is { } 1 , 1 , 1 , 1 ] [ = n h . (a) Find (expressed in sequence form) and sketch the output ] [ n y when the input is { } 1 , 1 , 1 , 1 ] [ = n x . (b) Find (in sequence form) and sketch the output ] [ 1 n y when the input is ] 1 [ ] [ ] [ 1 - - = n x n x n x . (c) Find (in sequence form) and sketch the output signal, ] 1 [ ] [ ] [ 2 - - = n y n y n y . (d) Is the following TRUE or FALSE? Suppose the input, ] [ n x , of a discrete-time, LTI system produces an output ] [ n y . Then the first-order backward difference of the original input, ] [ n x , i.e., ] 1
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