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0.2 N = 13 winograd fft module

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A very efficient length N = 13 FFT module that can be use alone or with the PFA or the WFTA. Designed by Howard Johnson in 1981.

N=13 fft module

A FORTRAN implementation of a length-13 FFT module to be used in a Prime Factor Algorithm program.

C DATA C131, C132 / 1.08333333, 0.30046261 /DATA C133, C134 / 0.74927933, 0.40113213 / DATA C135, C136 / 0.57514073, 0.52422664 /DATA C137, C138 / 0.51652078, 0.00770586 / DATA C139, C1310/ 0.42763400, 0.15180600 /DATA C1311,C1312/ 0.57944000, 1.15439534 / DATA C1313,C1314/ 0.90655220, 0.81857027 /DATA C1315,C1316/ 1.19713677, 0.86131171 / DATA C1317,C1318/ 1.10915484, 0.04274143 /DATA C1319,C1320/ 0.04524049, 0.29058457 / CC------------------WFTA N=13-------------------------------- C113 A1 = X(I(2)) + X(I(13)) A2 = X(I(3)) + X(I(12))A3 = X(I(4)) + X(I(11)) A4 = X(I(5)) + X(I(10))A5 = X(I(6)) + X(I(9)) A6 = X(I(7)) + X(I(8))A7 = X(I(2)) - X(I(13)) A8 = X(I(3)) - X(I(12))A9 = X(I(4)) - X(I(11)) A10 = X(I(5)) - X(I(10))A11 = X(I(6)) - X(I(9)) A12 = X(I(7)) - X(I(8))B1 = Y(I(2)) + Y(I(13)) B2 = Y(I(3)) + Y(I(12))B3 = Y(I(4)) + Y(I(11)) B4 = Y(I(5)) + Y(I(10))B5 = Y(I(6)) + Y(I(9)) B6 = Y(I(7)) + Y(I(8))B7 = Y(I(2)) - Y(I(13)) B8 = Y(I(3)) - Y(I(12))B9 = Y(I(4)) - Y(I(11)) B10 = Y(I(5)) - Y(I(10))B11 = Y(I(6)) - Y(I(9)) B12 = Y(I(7)) - Y(I(8))A13 = A2 + A5 + A6 A14 = A1 + A3 + A4A15 = A13 + A14 A16 = A8 + A11 + A12A17 = A7 + A9 - A10 A18 = A2 - A6A19 = A3 - A4 A20 = A1 - A4A21 = A5 - A6 A22 = A18 - A19A23 = A20 - A21 A24 = A18 + A19A25 = A20 + A21 A26 = A8 - A12A27 = A7 - A9 A28 = A8 - A11A29 = A7 + A10 A30 = A11 - A12A31 =-A9 - A10 B13 = B2 + B5 + B6B14 = B1 + B3 + B4 B15 = B13 + B14B16 = B8 + B11 + B12 B17 = B7 + B9 - B10B18 = B2 - B6 B19 = B3 - B4B20 = B1 - B4 B21 = B5 - B6B22 = B18 - B19 B23 = B20 - B21B24 = B18 + B19 B25 = B20 + B21B26 = B8 - B12 B27 = B7 - B9B28 = B8 - B11 B29 = B7 + B10B30 = B11 - B12 B31 =-B9 - B10AM0 = X(I(1)) + A15 AM2 = (A13 - A14) * C132AM5 = (A16 + A17) * C135 AM6 = A22 * C136AM7 = A23 * C137 AM8 = (A22 + A23) * C138AM9 = A24 * C139 AM10 = A25 * C1310AM11 = (A24 - A25) * C1311 AM14 = (A26 + A27) * C1314AM17 = (A28 + A29) * C1317 AM20 = (A30 + A31) * C1320BM0 = Y(I(1)) + B15 BM2 = (B13 - B14) * C132BM5 = (B16 + B17) * C135 BM6 = B22 * C136BM7 = B23 * C137 BM8 = (B22 + B23) * C138BM9 = B24 * C139 BM10 = B25 * C1310BM11 = (B24 - B25) * C1311 BM14 = (B26 + B27) * C1314BM17 = (B28 + B29) * C1317 BM20 = (B30 + B31) * C1320CC0 = AM0 - A15 * C131 CC1 = AM7 + AM6 - AM2CC2 = AM7 + AM8 + AM2 CC3 = AM8 - AM6 - AM2CC4 = CC0 + AM9 + AM10 CC5 = CC0 - AM10 - AM11CC6 = CC0 - AM9 + AM11 CC7 = AM14 - A26 * C1312CC8 = AM14 - A27 * C1313 CC9 = -AM17 + A28 * C1315CC10 = -AM17 + A29 * C1316 CC11 = AM20 - A30 * C1318CC12 = AM20 + A31 * C1319 CC13 = -AM5 + A16 * C133CC14 = -AM5 + A17 * C134 CC15 = CC1 + CC4CC16 = CC2 + CC5 CC17 = CC5 - CC2CC18 = CC3 + CC6 CC19 = CC4 - CC1CC20 = CC6 - CC3 CC21 = CC14 + CC7 + CC9CC22 = CC10 - CC12 + CC13 CC23 =-CC7 - CC11 + CC14CC24 = CC9 - CC11 - CC14 CC25 = CC8 + CC12 + CC13CC26 = CC13 - CC8 - CC10 DD0 = BM0 - B15 * C131DD1 = BM7 + BM6 - BM2 DD2 = BM7 + BM8 + BM2DD3 = BM8 - BM6 - BM2 DD4 = DD0 + BM9 + BM10DD5 = DD0 - BM10 - BM11 DD6 = DD0 - BM9 + BM11DD7 = BM14 - B26 * C1312 DD8 = BM14 - B27 * C1313DD9 = -BM17 + B28 * C1315 DD10 = -BM17 + B29 * C1316DD11 = BM20 - B30 * C1318 DD12 = BM20 + B31 * C1319DD13 = -BM5 + B16 * C133 DD14 = -BM5 + B17 * C134DD15 = DD1 + DD4 DD16 = DD2 + DD5DD17 = DD5 - DD2 DD18 = DD3 + DD6DD19 = DD4 - DD1 DD20 = DD6 - DD3DD21 = DD14 + DD7 + DD9 DD22 = DD10 - DD12 + DD13DD23 =-DD7 - DD11 + DD14 DD24 = DD9 - DD11 - DD14DD25 = DD8 + DD12 + DD13 DD26 = DD13 - DD8 - DD10X(I(1)) = AM0 X(I(2)) = CC15 - DD21X(I(3)) = CC16 - DD22 X(I(4)) = CC17 - DD23X(I(5)) = CC18 - DD24 X(I(6)) = CC19 - DD25X(I(7)) = CC20 - DD26 X(I(8)) = CC20 + DD26X(I(9)) = CC19 + DD25 X(I(10)) = CC18 + DD24X(I(11)) = CC17 + DD23 X(I(12)) = CC16 + DD22X(I(13)) = CC15 + DD21 Y(I(1)) = BM0Y(I(2)) = CC21 + DD15 Y(I(3)) = CC22 + DD16 Y(I(4)) = CC23 + DD17Y(I(5)) = CC24 + DD18 Y(I(6)) = CC25 + DD19Y(I(7)) = CC26 + DD20 Y(I(8)) =-CC26 + DD20Y(I(9)) =-CC25 + DD19 Y(I(10)) =-CC24 + DD18Y(I(11)) =-CC23 + DD17 Y(I(12)) =-CC22 + DD16Y(I(13)) =-CC21 + DD15 CGOTO 20 CFigure: Length-13 FFT Module

Questions & Answers

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Source:  OpenStax, Large dft modules: 11, 13, 16, 17, 19, and 25. revised ece technical report 8105. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10569/1.7
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