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By John R. Buck

Designed to increase larger figuring out of the rules of signs and structures. makes use of MATLAB routines to actively problem the reader to use mathematical strategies to genuine global difficulties.

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C). 8y[n- 11 = 2x[n- 11. (d). You should begin by defining the vector x= C1 2 3 41, which contains x[n]on the interval 1 5 n 4. The result of using f i l t e r for each system is shown below. 5, you can see that f i l t e r has set x[0]and x[-11 equal to zero, since both of these samples are needed to determine yl [ l ] . 24 CHAPTER 2. LINEAR TIME-INVARIANT SYSTEMS The function f i l t e r can also be used to perform discrete-time convolution. Consider the class of systems satisfying Eq. 7) when an = b [ k ] .

A3(32)], so you will need to determine which elements of a correspond to the negative values of k when you implement the sums. (g). Argue that x3-,n[n] must be a real signal. (h). Generate a sequence of appropriately labeled plots using stem showing how the signals you created converge to x3[n] as more of the DTFS coefficients are included in the sum. Specifically, x3-all should be equal t o the original vector x3 within the bounds of MATLAB's roundoff error. Does the synthesis of this discrete-time square wave display the Gibb's phenomenon?

If not, this means the result of processing a signal with the series connection of Systems 1 and 2 is not equal to the result of processing the signal with a single system whose impulse response is the convolution of the impulse response of System 1 with the impulse response of System 2. Does this violate the associative property of convolution as discussed in Part (d)? (g). Consider the parallel connection of two systems; call them System 1 and System 2. System 2 is an LTI system with impulse response hg2[n]= h ~ [ nas] defined in Part (a).

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