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Thus, the ROC and the pole-zero plot for this example are shown in Fig. 4-2. Comparing Eqs. (4.9) and (4.12) [or Eqs. (4.10) and (4.13)], we see that the algebraic expressions of X ( z ) for two different sequences are identical except for the ROCs. Thus, as in the Laplace
(a) Put the calculator in degree mode. (b) Enter 0.8163, press (inv) key, and press (cos) key. (c) A 35.28 to the nearest hundredth degree OR
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The rst step in LOC-based estimation is to estimate the number of lines of code in the nished project. This can be done based on experience, size of previous pro-
C. Properties of the ROC: As we saw in Examples 4.1 and 4.2, the ROC of X ( z ) depends on the nature of x [ n ] . The properties of the ROC are summarized below. We assume that X ( Z ) is a rational function of z.
Property 1 : Property 2:
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jects, size of a competitor s solution, or by breaking down the project into smaller pieces and then estimating the size of each of the smaller pieces. A standard approach is, for each piecei, to estimate the maximum possible size, maxi, the minimum possible size, mini, and the best guess size, besti. The estimate for the whole project is 1/6 of the sum of the maximums, the minimums, and 4 times the best guess: Standard deviation of S sd 2 sd 2 . . . sd 2 1=2 Standard deviation of E i max min =6
(d) Record the whole number of degrees, 35 . (e) Press ( ) key, enter 35, press ( ) key, press ( ) key, enter 60, and press ( ) key. (f) To the nearest minute, the displayed value is 17 . (g) A 35 17 to the nearest minute.
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The ROC does not contain any poles. If x [ n ] is a finite sequence (that is, x [ n ] = 0 except in a finite interval N l ~ n s N,, where N , and N , are finite) and X(z) converges for some value of z, then the ROC is the entire z-plane except possibly z = 0 or z = co. If x [ n ] is a right-sided sequence (that is, x [ n ] = 0 for n < N, < 03) and X(z) converges for some value of z, then the ROC is of the form
Team WRT had identified seven subpieces to their project. These are shown in Table 4-4 with their estimates of the size of each subpiece. Table 4-4 Part 1 2 3 4 5 6 7 Subpiece Size Estimate (in LOC) Best Guess 30 15 30 35 20 12 22 Min Size 50 25 45 40 25 14 25
Property 3:
The estimates for each section are as follows: p1 20 4 30 50 =6 190=6 31:6 p2 10 4 15 25 =6 95=6 15:8 p3 25 4 30 45 =6 190=6 31:6 p4 30 4 35 40 =6 220=6 36:7 p5 15 4 20 25 =6 120=6 20 p6 10 4 12 14 =6 72=6 12 p7 20 4 22 25 =6 133=6 22:17 The estimate for the whole project is the sum of the estimates for each section: Whole 31:6 15:8 31:6 36:7 20 12 22:17 170:07 LOC
where r,, equals the largest magnitude of any of the poles of X(z). Thus, the ROC is the exterior of the circle lzl= r,, in the z-plane with the possible exception of z = m.
When values of cotangent, secant, or cosecant are given, the reciprocal of the given function value is found, and then the reciprocal function is used.
Property 4:
The estimate for the standard deviation of the estimate is as follows: Standard deviation 50 20 2 25 10 2 45 25 2 40 30 2 25 15 2 14 10 2 25 20 2 :5 900 225 400 100 100 16 25 :5 1766:5 42:03
If x [ n ] is a left-sided sequence (that is, x [ n l = 0 for n > N , > for some value of z, then the ROC is of the form
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