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1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5.

1.18. Consider a discrete-time system with input x[n] and output y[n] related by yn] * x[k], k%3Dnールの where no is a finite positive integer. (a) Is this system linear? (a) Is this system time-invariant? (c) If x[n] is known to be bounded by a finite integer B (i.e., lx[n] < B for all n), it can be shown that y[n] is bounded by a finite number C. We conclude that the given system is stable. Express C in terms of B and no.

1.38. In this problem, we examine a few of the properties of the unit impulse function (a) Show that Hint: Examine δΔ(1). (See Figure 1.34.) (b) In Section 1.4, we defined the continuous-time unit impulse as the limit of the signal δΔ(t). More precisely, we defined several of the properties of δ(t) by examining the corresponding properties of δΔ(t). For example, since the signal Signals and Systems Chap. 1 converges to the unit step u(t) - lim ua(t), (P1.38-1) we could interpret δ(t) through the equation or by viewing δ(t) as the formal derivative of u(t) This type of discussion is important, as we are in effect trying to define 6(t) through its properties rather than by specifying its value for each t, which is not possible. In Chapter 2, we provide a very simple characterization of the behavior of the unit impulse that is extremely useful in the study of linear time- invariant systems. For the present, however, we concentrate on demonstrating that the important concept in using the unit impulse is to understand how it behaves. To do this, consider the six signals depicted in Figure P1.38. Show l(t) r2(t) -스 Δ2a