# 0.1 N = 11 winograd fft module

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A very efficient length N = 11 FFT module that can be use alone or with the PFA or the WFTA. Designed by Howard Johnson in 1981.

## N=11 fft module

A FORTRAN implementation of a length-11 FFT module to be used in a Prime Factor Algorithm program.

```C DATA C111,C112 / 1.10000000, 0.33166250 /DATA C113,C114 / 0.51541500, 0.94125350 / DATA C115,C116 / 1.41435370, 0.85949300 /DATA C117,C118 / 0.04231480, 0.38639280 / DATA C119,C1110/ 0.51254590, 1.07027569 /DATA C1111,C1112/ 0.55486070, 1.24129440 / DATA C1113,C1114/ 0.20897830, 0.37415717 /DATA C1115,C1116/ 0.04992992, 0.65815896 / DATA C1117,C1118/ 0.63306543, 1.08224607 /DATA C1119,C1120/ 0.81720738, 0.42408709 / CC-----------------WFTA N=11---------------------------- C111 T1 = X(I(2)) + X(I(11)) T6 = X(I(2)) - X(I(11))T2 = X(I(3)) + X(I(10)) T7 = X(I(3)) - X(I(10))T3 = X(I(4)) + X(I(9)) T8 = X(I(4)) - X(I(9))T4 = X(I(5)) + X(I(8)) T9 = X(I(5)) - X(I(8))T5 = X(I(6)) + X(I(7)) T10= X(I(6)) - X(I(7))C U1 = Y(I(2)) + Y(I(11))U6 = Y(I(2)) - Y(I(11)) U2 = Y(I(3)) + Y(I(10))U7 = Y(I(3)) - Y(I(10)) U3 = Y(I(4)) + Y(I(9))U8 = Y(I(4)) - Y(I(9)) U4 = Y(I(5)) + Y(I(8))U9 = Y(I(5)) - Y(I(8)) U5 = Y(I(6)) + Y(I(7))U10= Y(I(6)) - Y(I(7)) CT11 = T1 + T2 T12 = T3 + T5T13 = T4 + T11 + T12 T14 = T7 - T8T15 = T6 + T10 CU11 = U1 + U2 U12 = U3 + U5U13 = U4 + U11 + U12 U14 = U7 - U8U15 = U6 + U10 CAM0 = X(I(1)) + T13 AM2 = (T14 - T15 - T9) * C112AM3 = (T2 - T4) * C113 AM4 = (T1 - T4) * C114AM5 = (T2 - T1) * C115 AM6 = (T5 - T4) * C116AM7 = (T3 - T4) * C117 AM8 = (T5 - T3) * C118AM11 = (T12 - T11) * C1111 AM14 = (T6 + T7) * C1114AM17 = (T8 - T10) * C1117 AM20 = (T14 + T15) * C1120C AN0 = Y(I(1)) + U13AN2 = (U14 - U15 - U9) * C112 AN3 = (U2 - U4) * C113AN4 = (U1 - U4) * C114 AN5 = (U2 - U1) * C115AN6 = (U5 - U4) * C116 AN7 = (U3 - U4) * C117AN8 = (U5 - U3) * C118 AN11 = (U12 - U11) * C1111AN14 = (U6 + U7) * C1114 AN17 = (U8 - U10) * C1117AN20 = (U14 + U15) * C1120 CS0 = AM0 - C111 * T13 S7 = AM11 + C1110 * (T1 - T3)S8 = AM11 + (T2 - T5) * C119 S9 = AM14 + (T6 - T9) * C1113S10 =-AM14 + (T7 + T9) * C1112 S11 = AM17 + (T8 - T9) * C1116S12 =-AM17 + (T9 - T10) * C1115 S13 = AM20 + (T6 - T8) * C1119S14 =-AM20 + (T7 + T10) * C1118 CV0 = AN0 - C111 * U13 V7 = AN11 + C1110 * (U1 - U3)V8 = AN11 + (U2 - U5) * C119 V9 = AN14 + (U6 - U9) * C1113V10 =-AN14 + (U7 + U9) * C1112 V11 = AN17 + (U8 - U9) * C1116V12 =-AN17 + (U9 - U10) * C1115 V13 = AN20 + (U6 - U8) * C1119V14 =-AN20 + (U7 + U10) * C1118 CS15 = S0 + S7 + AM7 + AM8 S16 = S0 - S7 - AM4 - AM5S17 = S0 + S8 + AM6 - AM8 S18 = S0 - S8 - AM3 + AM5S19 = S0 + AM3 + AM4 - AM6 - AM7 S20 = S13 + AM2 + S11S21 = S13 - AM2 - S9 S22 = S14 + AM2 + S12S23 = S14 - AM2 - S10 S24 = S9 + S10 + S11 + S12 - AM2C V15 = V0 + V7 + AN7 + AN8V16 = V0 - V7 - AN4 - AN5 V17 = V0 + V8 + AN6 - AN8V18 = V0 - V8 - AN3 + AN5 V19 = V0 + AN3 + AN4 - AN6 - AN7V20 = V13 + AN2 + V11 V21 = V13 - AN2 - V9V22 = V14 + AN2 + V12 V23 = V14 - AN2 - V10V24 = V9 + V10 + V11 + V12 - AN2 CX(I(1)) = AM0 X(I(2)) = S19 + V24X(I(3)) = S15 + V20 X(I(4)) = S16 + V21X(I(5)) = S17 - V22 X(I(6)) = S18 + V23X(I(7)) = S18 - V23 X(I(8)) = S17 + V22X(I(9)) = S16 - V21 X(I(10))= S15 - V20X(I(11))= S19 - V24 CY(I(1)) = AN0 Y(I(2)) = V19 - S24Y(I(3)) = V15 - S20 Y(I(4)) = V16 - S21Y(I(5)) = V17 + S22 Y(I(6)) = V18 - S23Y(I(7)) = V18 + S23 Y(I(8)) = V17 - S22Y(I(9)) = V16 + S21 Y(I(10))= V15 + S20Y(I(11))= V19 + S24 CGOTO 20 CFigure. Length-11 FFT Module```

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
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
characteristics of micro business
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
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
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