# 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```

are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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