# 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```

so some one know about replacing silicon atom with phosphorous in semiconductors device?
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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