HP 50g Graphing, 48gII Graphing manual Fdistrib, Fft, Cf, Fc?, Fs? Fs?C, Sf, Distrib

Input/Output:

		Level 1/Argument 1			Level 1/Item 1
		nflag number		→	0/1
	If flag –44 is
Example:		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)(X1)(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	Command
Type:
Description:	Discrete Fourier Transform Command: Computes the one or twodimensional discrete Fourier
	transform of an array.
	If the argument is an Nvector or an		N × 1 or 1 × N matrix, FFT computes the onedimensional
	transform. If the argument is an M × N matrix, FFT computes the twodimensional transform . M
	and N must be integral powers of 2.
	The onedimensional discrete Fourier transform of an Nvector				X is the Nvector Y where:
		– 1	2πikn
			–---------------
		Yk = ∑ Xne		, i = –1

n = 0

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:

			M – 1	– 1		2πikm	e–	2πi ln
						e–----------------M
Y	kl	=	∑ ∑ x		mn			----------------- ,i = –1
			m = 0	n = 0

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 15digit arithmetic and intermediate storage, then rounds the result to 12digit precision.

386 Full Command and Function Reference