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522 MUSICAL ApPLICATIONS OF MICROPROCESSORS<br />

serious alias distortion is to be avoided. The finite maximum attenuation<br />

means that some noise will be introduced by the interpolation. It is also<br />

possible to "tail <strong>of</strong>f" the ends <strong>of</strong> the impulse response rather than truncate it.<br />

The effect <strong>of</strong> this is to increase the maximum attenuation at the expense <strong>of</strong><br />

decreasing the cut<strong>of</strong>f slope. This means that if the input data is adequately<br />

oversampled, either the interpolation noise may be reduced or fewer points<br />

may be used in the interpolation. Tailing <strong>of</strong>f will be discussed further in<br />

Chapter 16.<br />

The Table Method <strong>of</strong>Interpolation<br />

Even when the number <strong>of</strong> points is reduced to a reasonable value, the<br />

sine functions and divisions necessary to apply the method are very time<br />

SECTION 1 SECTION 2 SECTION 3 SECTION 4 SECTION 5 SECTION 6<br />

ADDR DATA ADDR DATA ADDR DATA ADDR DATA ADDR DATA ADDR DATA<br />

0 .00000 32 .00000 64 .00000 96 .00000 128 .00000 160 .00000<br />

1 .99833 33 -.02819 65 .01157 97 -.00527129 .00211 161 -.00062<br />

2 .99333 34 -.05422 66 .02247 98 -.01023 130 .00407 162 -.00119<br />

3 .98504 35 -.07801 67 .03263 99 -.01483 131 .G0587 163 -.00169<br />

4 .97349 36 -.09952 68 .04198 100 -.01905132 .00748 164 -.00213<br />

5 .95878 37 -.11870 69 .05047 101 -.02286 133 .00891 165 -.00251<br />

6 .94099 38 -.13554 70 .05805 102 -.02624 134 .01015 166 -.00282<br />

7 .92022 39 -.15004 71 .06470 103 -.02918 135 .01120 167 -.00308<br />

8 .89662 40 -.16220 72 .07039 104 -.03167 136 .01206 168 -.00328<br />

9 .87032 41 -.17207 73 .07511 105 -.03371 137 .01274 169 -.00343<br />

10 .84150 42 -.17968 74 .07887 106 -.03530 138 .01322 170 -.00353<br />

11 .81032 43 -.18510 75 .08165 107 -.03644 139 .01354 171 -.00358<br />

12 .77698 44 -.18840 76 .08349 108 -.03715 140 .01368 172 -.00358<br />

13 .74168 45 -.18967 77 .08441 109 -.03744 141 .01366 173 -.00355<br />

14 .70464 46 -.18902 78 .08444 110 -.03732 142 .01350 174 -.00348<br />

15 .66607 47 -.18654 79 .08364 111 -.03684 143 .01320 175 -.00339<br />

16 .62621 48 -.18237 80 .08203 112 -.03599 144 .01277 176 -.00326<br />

17 .58528 49 -.17663 81 .07967 113' -.03482 145 .01224 177 -.00311<br />

18 .54354 50 -.16956 82 .07663 114 -.03336 146 .01161 178 -.00295<br />

19 .50121 51 -.16099 83 .07297 115 -.03163 147 .01090 179 -.00276<br />

20 .45854 52 -.15138 84 .06875 116 -.02967 148 .01012 180 -.00257<br />

21 .41577 53 -.14077 85 .06404 117 -.02751 149 .00928 181 -.00237<br />

22 .37312 54 -.12931 86 .05891 118 -.02519150 .00841 182 -.00216<br />

23 .33084 55 -.11716 87 .05344 119 -.02273 151 .00751 183 -.00194<br />

24 .29814 56 -.10446 88 .04769 120 -.02019152 .00660 184 -.00173<br />

25 .24824 57 -.09137 89 .04174 121 -.01757 153 .00568 185 -.00151<br />

26 .20834 58 -.07801 90 .03565 122 -.01493 154 .00477 186 -.00129<br />

27 .16964 59 -.06455 91 .02951 123 -.01229 155 .00388 187 -.00107<br />

28 .13232 60 -.05111 92 .02337 124 -.00967156 .00302 188 -.00085<br />

29 .09655 61 -.03781 93 .01728 125 -.00711 157 .00219 189 -.00063<br />

30 .06248 62 -.0247994 .01132 126 -.00463 158 .00141 190 -.00042<br />

31 .03026 63 -.01215 95 .00555 127 -.00255 159 .00068 191 -.00021<br />

192 .00000<br />

Fig. 14-31. Interpolation table

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