http://library.lanl.gov/numerical/bookcpdf/c12-2.pdf   FFT

Fast Fourier Transform methods are described in the HP part of my url.
It finds the frequency components of a repeated wave form  given amplitudes at N=8 time intervals.
Create a folder called FT in Var-Link. In MODE, select Degree\
Select Float 12 in MODE or computation will be only approaximate
In Home create an equation 2+0.9*Sin(x)+0.8*Cos(x)+0.7*Sin(2*x)+0.6*Cos(2*x) ->z
k0 = 2  k1 = 0.9   k2 = 0.8  k3 = 0.7  k4 = 0.6  
Create this table

tt          time(approx)           frequency(approx)
x=Angle     y=value 
0          3.4    = m1       16         = n1
45         3.902  = m2       3.2-3.6*i  = n2
90         2.3    = m3       2.4-2.8*i  = n3
135        1.3707 = m4       0+0*i      = n4
180        1.8    = m5       0+0*i      = n5
225        1.4979 = m6       0+0*i      = n6
270        0.5    = m7       2.4+2.8*i  = n7
315        1.229  = m8       3.2+3.6*i  = n8

{ 3.4 , 3.902 , 2.3 , 1.3707 , 1.8 , 1.4979 , 0.5 , 1.229 }

x->value   z  see value of m, store value as m1...m8

Select APPS   EEPro   F2    6:Fourier Transform  1:FFT
Time  Enter   {m1,m2,m3,m4,m5,m6.m7.m8}    
See Time{3.4,3.902....1.229}  Use full accuracy
Select Freq  F2  See {16,3.2-3.6*i...3.2+3.6*i} Yellow COPY  See above
Right arrow and F4 expands display

DelVar x to see equation z unevaluated

16/8=2 =k0  3.6/4 =0.9 = k1  3.2/4=0.8 = k2   2.8/4 = k3  2.4/4= 0.6 = k4
8=number of samples   4=number of samples/2

Use n1 and final data n7,n8.  If more frequencies are present x ,2*x,3*x, use only n6 n7 n8.  Use 16,32, 64,... points for more frequencies.

Hit ESC Choose 2:Inverse FFT Enter
It finds the Time components of a repeated wave form given frequencies.
Paste Frequency List {{16,.3.2....}
Select time   F2  See {3.4+0*i,3.902+0*i+....+1.229+0*i}

on HOME Paste list of time values in HOME
You can store values of time  { delete   3.4 -> m1 (delete comma) (add :) 
3.902 -> m2: ...m8     (delete }) ENTER
Now plot curve and points
Home    post z   See equation.  darken with both up arrows and COPY

APPS  Select Data/Matrix  Enter  3:New   Type  Data Folder ft Variable zz
Enter
Under C1 post 0 45. 90. ...315
Under C2 post m1 m2 m3   ... m8  see values

HOME Yellow y1=PASTE  Enter  see equation  .6*Cos(2.0000....
Go to Plot1  Enter    Scatter Box   x=c1  y=c2  Enter  
Yellow Window xmin=0   xmax = 360 xscl=1 ymin =.45   ymax =  4
yscl=1   xres =1 
Yellow Graph
See curve with selected points as boxes
===
seq(x.x,0,7) makes {0 1 2 3 4 5 6 7}

Program to compute FFT
@ is optional
Make a folder labeled afft

Create a program titled fft
Program will be shown with only 4 digit accuracy in the input.
Paste a list with full accuaracy.

fft()
Prgm
ClrIO
0->n
{}->zzz
{}->s
-0.25*Pi*i->u
{ 3.4 , 3.902 , 2.3 , 1.3707 , 1.8 , 1.4979 , 0.5 , 1.229 } -> g
{ 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 } -> a
While n<8
For t,0,7,1
   @Disp "t",t
   @Disp "n",n
   @Pause
   @ClrIO
mid(a,n+1,1) -> c
   @Disp "c",c
t*c*u -> d
   @Disp "d",d
e^(d) -> ps
   @Disp "ps",ps
   @Pause
   @ClrIO
mid(g,t+1,1) -> q
   @Disp "q",q
ps*q -> y
   @Disp "y",y
   @Pause
   @ClrIO
augment(s,y) -> s
   @Disp "s",s
   @Pause
   @ClrIO
EndFor
   @Disp "s",s
sum(s) -> zz
   @Disp "zz",zz
   @Pause
   @ClrIO
augment(zzz,{zz}) -> zzz
   @Disp "zzz",zzz
{} -> s
n+1->n
EndWhile
Disp "zzz",zzz
EndProgram

See
{ 16  3.2 - 3.6*i  2.4 - 2.8*i  0 + 0*i  0 + 0*i  0 + 0*i  2.4 + 2.8*i   3.2 + 3.6*i }
Which is FFT data

================
 Create a program named ifft

Create a program titled fft
Program will be shown with only 4 digit accuracy in the input.
Paste a list with full accuaracy.
fft()

ifft()
Prgm
ClrIO
0->n
{}->zzz
{}->s
+0.25*Pi*i->u
{ 16  3.2 - 3.6*i  2.4 - 2.8*i  0 + 0*i  0 + 0*i  0 + 0*i  2.4 + 2.8*i   3.2 + 3.6*i } -> g
{ 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 } -> a
While n<8
For t,0,7,1
   @Disp "t",t
   @Disp "n",n
   @Pause
   @ClrIO
mid(a,n+1,1) -> c
   @Disp "c",c
t*c*u -> d
   @Disp "d",d
e^(d) -> ps
   @Disp "ps",ps
   @Pause
   @ClrIO
mid(g,t+1,1) -> q
   @Disp "q",q
ps*q -> y
   @Disp "y",y
   @Pause
   @ClrIO
augment(s,y) -> s
   @Disp "s",s
   @Pause
   @ClrIO
EndFor
   @Disp "s",s
sum(s) -> zz
   @Disp "zz",zz
   @Pause
   @ClrIO
augment(zzz,{zz}) -> zzz
   @Disp "zzz",zzz
{} -> s
n+1->n
EndWhile
zzz/8 -> fin
Disp "fin",fin
EndPrgm

See
{ 3.4 + 0*i, 3.902 + 0*i , 2.3 + 0*i , 1.3707 + 0*i , 1.8 + 0*i ,
 1.4979 + 0*i , 0.5 + 0*i , 1.229 + 0*i }
This is time amplitude data