RM0020 datasheet(24/69 Pages) STMICROELECTRONICS

24 / 69 page

Function API

RM0020

24/69

Here is the summary how the real to complex float in-place FFT can be calculated

using the split function:

–

on real input data in_Re(0) in_Re(1) ... in_Re(N-1), calculate complex to

complex FFT of half the length

–

call the split function which calculates the half of the spectrum X_Re(0) X_Im(0)

X_Re(1) X_Im(1) ... X_Re(N/2-1) X_Im(N/2-1)

–

if N2_REALPART is defined to 1, the split function saves the X_Re(N/2) into

X_Im(0)

Algorithm:

Input data in memory:

, Re - real part, Im -

imaginary part

Equation 9

The split function performs calculation of the output sequence

from the input

sequence

according to the following equations:

Equation 10

Equation 11

Equation 12

for each k from 1 to N/2-1

where:

Equation 13

Equation 14

Equation 15

* denotes complex conjugate operation

i is the imaginary unit

Equation 16

output data in memory:

when

N2_REALPART is defined to 0

when

N2_REALPART is defined to 1

x_Re 0

x_Im 0

x_Re 1

x_Im 1

x_Re N

---- 1

–





x_Im

---- 1

–







x_Re k

 ix_Im k



x_Re 0

 x_Im 0



----





x_Re 0

 x_Im 0



–



wa k

xk

 wb k

x

* N

---- k

–





wa k



--- 1iW

–





wb k



--- 1iW







------

–



X_Re k

 iX_Im k



X_Re 0

X_Im 0

X_Re 1

X_Im 1

X_Re N

---- 1

–





X_Im

---- 1

–





X_Re 0

X_Re N

----





X_Re 1

X_Im 1

X_Re N

---- 1

–





X_Im

---- 1

–





RM0020 Datasheet(PDF) 24 Page - STMicroelectronics

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