# 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```

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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