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AIII. BASIC Program for Long Division
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The BASIC program given in Fig. 23.7 is useful to invert a Z-transform by the method of long division. To use the program, one must arrange the Z-transform C(z) in the form a0 + qz- + u*z-2 + *+a umz(23.38) C(z) = 1 + brz- + b2z-2 + ... b,z- When the computer program is run, one enters the values of ua, a 1, . . . , b 1, h, . . . , m, and n when requested by the program. One also enters the number of terms desired in the long division. To illustrate the use of the program, we shall do the long division that was done in Example 23.1. After introducing the parameters of Example 23.1 into Eq. (23.11), C(z) becomes C(z) = 1 + 2z- + 2-2 z - 0.368
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To put this in the form of Eq. (23.38), multiply numerator and denominator by z - and the result is z-l + 2z-* + 2-3 C(z) = 1 - 0.36&- From the numerator of this expression, we see that ua = 0, ur = 1, u2 = 2, us = 1, and m = 3. From the denominator, we see that bl = -0.368 and n = 1. Introducing these values into the sample run shown in Table 23.2 gives a result that agrees with that of Example 23.1.
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5 DIM A(20), B(20), X(20), D(20) LO PRINT "Z-TRANSFORM INVERSION BY LONG DIVISION" LS PRINT 20 PRINT "ORDER OF NUHERATIOR, H": INPUT H 25 PRINT 30 PRINT "INPUT NUMERATOR COEFFICIENTS A OF THE FORM:" '40 PRINT "AU + AL/Z**L + A2/Z**2 + . . . + AH/Z**B" 50 FOR I = 0 TO 11 btl PRINT "COEFFICIENT", I: INPUT A(I) 70 NEXT I 75 PRINT 80 PRINT "ORDER OF DENOHINATOR,N": INPUT N 85 PRINT 90 PRINT "INPUT OF DENOMINATOR COEFFICIENTS,B, OF TRE FORM:" LOO PRINT "I, + BL/Z**L + B2/Z**2 + . . . + BN/Z**N" 1LO PRINT "NOTE THAT BO = la" I120 FOR I = L TO N 130 PRINT "COEFFICIENT", I: INPUT B(I) I140 NEXT I It'+2 PRINT 143 PRINT "BOW MANY TERMS DO YOU WANT IN TiiE INVERSE FORE " I,45 PRINT "CO + CL/Z**1 + C2/Z**2 + . . . + CJ/Z**J" 147 INPUT N3 I,50 NL = N: IF H>N TIiEN NL=H ZbO FOR I = I TO N1 I170 D(I) = A(I) la80 IF I>N TEEN B(I) = 0 190 IF I>H THEN D(I) =O 200 NEXT I 210 D(NL+L) = 0 220 IF A(O) = 0 GOT0 270 230 X(O) = A(O) 2'+0 FOR I = II TO N: D(I) = D(I) - X(O)*B(I): NEXT I 250 X(1) = D(l) 260 GOT0 280 270 X(O) = 0: X(L) = A(L) 280 PRINT X(O),"/Z** 0 +" 282 PRINT X(L),"/Z** L +" 288 FOR J = 2 TO N3 290 FOR K = II TO IL: D(K) = D(K+L) - X(J-L)*B(K): NEXT K 300 X(J) = D(L) 3LO PRINT X(J),"Z/**";J;"+" 320 NEXT J 330 END
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FIGURE 23-7 BASIC program for long division.
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TABLE 23.2
Output from a BASIC program for long division
RUN Z-TRANSFORH INVERSION BY LONG DIVISION ORDER OF NUHERATOR, I 3 INPUT NUMERATOR COEFFICIENTS A OF THE FORII: A0 + AL/Z**L + AZ/Z**2 + . . . +AU/Z**M COEFFICIENT 0 II COEFFICIENT ll II 2 COEFFICIENT 2 COEFFICIENT 3 1 ORDER OF DENOHINATOR,N I INPUT OF DENOMINATOR COEFFICIENTS, B, OF TEE FORM: I + BL/Z**L + B2/Z**2 + . . . + BN/Z**N NOTE TRAT BO = I COEFFICIENT In -.3b8 HOW MANY TERMS DO YOU WANT IN THE INVERSE FORM CO + CL/Z**L + Ci /Z**Z + . . . + CJ/Z**J 5 0 /z** Cl + II /Z** II + 2.3b8 /Z** 2 + ll.a7ltr124 /z** 3 + /Z** II + .b8Bb84 .25311357 /Z** 5 + Ok