Reference Guide
3-86 Full Command and Function Reference
Input/Output:
Level 1/Argument 1 Level 1/Item 1
n
flag number
→
0/1
Example: If flag –44 is set,
-44 FC?C
returns 0 to level 1 and clears flag –44.
See also: CF, FC?, FS? FS?C, SF
FDISTRIB
Type: Command
Description: Performs a full distribution of multiplication and division with respect to addition and subtraction
in a single step.
Access: !Ú
REWRITE
Input: An expression.
Output: An equivalent expression that results from fully applying the distributive property of
multiplication and division over addition and subtraction.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Expand
(X+1)(X-1)(X+2)
:
Command:
FDISTRIB((X+1)*(X-1)*(X+2))
Result:
X*(X*X)+2*(X*X)+(-(X*(1*X))+-(2*(1*X)))+ (X*(X*1)+2*(X*1)+
(-(X*(1*1))+-(2*(1*1))))
See also: DISTRIB
FFT
Type: Command
Description: Discrete Fourier Transform Command: Computes the one- or two-dimensional discrete Fourier
transform of an array.
If the argument is an N-vector or an N × 1 or 1 × N matrix, FFT computes the one-dimensional
transform. If the argument is an M × N matrix, FFT computes the two-dimensional transform. M
and N must be integral powers of 2.
The one-dimensional discrete Fourier transform of an N-vector X is the N-vector Y where:
Y
k
X
n
e
2πikn
---------------–
n 0=
1–
∑
= i, 1–=
for k = 0, 1, …, N – 1.
The two dimensional discrete Fourier transform of an M × N matrix X is the M × N matrix Y
where:
Y
kl
x
mn
e
2πikm
M
----------------–
e
2πi ln
------------------–
n 0=
1–
∑
m 0=
M 1–
∑
= i, 1–=
for k = 0, 1, …, M – 1 and l = 0, 1, …, N – 1.
The discrete Fourier transform and its inverse are defined for any positive sequence length.
However, the calculation can be performed very rapidly when the sequence length is a power of
two, and the resulting algorithms are called the fast Fourier transform (FFT) and inverse fast
Fourier transform (IFFT).
The FFT command uses truncated 15-digit arithmetic and intermediate storage, then rounds the
result to 12-digit precision.