FFT takes 2^n time history data points and computes the DC value and harmonics
oin the signal. Inverse FFT takes this information and computes time history
data points
Initial data.
Mode Radians 
Current Folder aft 
Mode Display Digits Float 6
Mode Approximate
Create a folder in Var-Link with the title aft.
Assume a time sequence defined by the formula 
2+.9*sin(x)+0.8*cos(x)+0.7*sin(2*x)+0.6*cos(2*x) -> teq
To see this graph,copy this equation to y1=2+.09*sin(x)...
Window xmin=0   xmax=7 ymin=0  ymax=5 Graph

Now create a list of 8 data points with this program in  folder aft.

yy()
Prgm
0->s
{}->zz
Pi/4=n
while s<8
s+n->x
teq->l
augment(zz,{l})->zz
s+1->s
EndWhile
Disp zz

go to Home
zz shows {3.4 3.902 ...1.229}
Copy this list by op arrow(copy button) then up cursor arrow.
See darkened equation.  

Mode main Enter
APPS EEPRO  F2 6: Fourier Transforms Enter
See 1: FFT    2: IFFT   Select FFT Enter   See Time:  Freq: Select Time
Diamond Paste   See list of data points
Hit F2   See Freq list 
Select Freq:  Right cursor arrow.  See list.  Small values are replaced 
here by zero
{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}
Enter returns to original screen
The DC value = 16/8 
Fundamental cosine(x) amplitude=3.2/4=0.8
Fundamental sine(x) amplitude=3.6/4=0.9
Second harmonic cosine(2*x) amplitude=2.4/4=0.6
Second harmonic sine(2*x) amplitude=2.8/4=0.7

Go to Inverse FFT by F1:8 Clear  F2:6    2:Inverse FFT
Note that list of harmonics is present.  F2   See Time sequence is computed.
Time:{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}

The theory is described in the HP FFT lesson.