## Developer Reference

• 2020
• 10/21/2020
• Public Content
Contents

# Packed Formats

This section describes the main packed formats
Perm
,
Pack
, and
CCS
used by the Fourier transform functions.

## Pack Format

The
Pack
format is a convenient, compact representation of a complex conjugate-symmetric sequence. The disadvantage of this format is that it is not the natural format used by the real Fourier transform algorithms (“natural” in the sense that bit-reversed order is natural for radix-2 complex Fourier transforms). In
Pack
format, the output samples of the Fourier transform are arranged as shown in the tables below. The output signal can be unpacked to a complex signal using the function
ippsConjPack
.

## Perm Format

The
Perm
format stores the values in the order in which the Fourier transform algorithms use them. This is the most natural way of storing values for the Fourier transform algorithms. The
Perm
format is an arbitrary permutation of the
Pack
format. An important characteristic of the
Perm
format is that the real and imaginary parts of a given sample need not be adjacent.
In
Perm
format, the output samples of the Fourier transform are arranged as shown in the tables below. The output signal can be unpacked to a complex signal using the function
ippsConjPerm
.
For input signal of odd length the perm and pack format are identical.

## CCS Format

The
CCS
format stores the values of the first half of the output complex signal resulted from the forward Fourier transform.
In
CCS
format, the output samples of the Fourier transform are arranged as shown in the tables below. Note that the signal stored in
CCS
format is one complex element longer. The output signal can be unpacked to a complex signal using the function
ippsConjCcs
.
Arrangement of Forward Fourier Transform Results in Packed Formats - Even Length
Index
0
1
2
3
. . .
N-2
N-1
N
N+1
Pack
R
0
R
1
I
1
R
2
. . .
I
(N-1)/2
R
N/2
Perm
R
0
R
N/2
R
1
I
1
. . .
R
N/2-1
I
N/2-1
CCS
R
0
0
R
1
I
1
. . .
R
N/2-1
I
N/2-1
R
N/2
0
Forward Fourier transform Result Representation in Packed Formats - Odd Length
Index
0
1
2
3
. . .
N-2
N-1
N
Pack
R
0
R
1
I
1
R
2
. . .
R
(N-1)/2
I
(N-1)/2
Perm
R
0
R
1
I
1
R
2
. . .
R
(N-1)/2
I
(N-1)/2
CCS
R
0
0
R
1
I
1
. . .
I
(N-1)/2-1
R
(N-1)/2
I
(N-1)/2

#### Product and Performance Information

1

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Notice revision #20110804