Information Technology Reference
In-Depth Information
high frequency side, are less perceptible. Therefore the candidate frame should be
chosen in segments that contain a significant amount of low frequency components.
Based on these considerations, a search routine can be developed, which identifies a
series of candidate frames in the host. Assume that each frame contains
N
samples:
s
= {
s
(0),
s
(1),
1)}, where
N
is chosen according to the required data rate and
the imperceptibility requirement.
The highest frequency component in the signal is
W
=
f
s
/2 where
f
s
is the sampling
frequency. Let
w
be the width of the frequency band occupied by watermark.
B
=
w
/
W
is the normalized watermark bandwidth. Each watermark unit takes a portion in the
spectrum of a signal frame lasting
T
=
N
/
f
s
seconds. When
f
s
= 44.1 kHz and
N
= 1024,
for example,
T
is 23.2ms.
In the present study, a band [
f
0
,
f
0
+
w
] where
f
0
=
w
=
W
/4 is used. Before embedding, a
test is performed to make sure that most of the spectral components in the band are
below an auditory masking threshold [10,11]. If this is not satisfied, the frame is
skipped, and the next frame that meets the condition is chosen.
…
,
s
(
N
−
2.2
Data Embedding
The proposed method uses dither modulation in the frequency domain. It may be
viewed as an application of the multi-carrier modulation technique OFDM. An
OFDM signal is composed of many equally spaced subcarriers within the occupied
band, which are modulated using various modulation schemes. Suppose there are
N
symbols,
X
(
n
),
n
= 0, 1, … ,
N
−
1, modulating
N
subcarriers respectively. The spacing
between subcarriers, T
f
, is chosen such that the subcarriers are mutually orthogonal
within one symbol period,
T
. The requirement of orthogonality is satisfied if
∆
∆
f
= 1/
T
.
Thus, subcarrier frequencies are
f
n
=
n
/
T
,
n
=0, 1, … ,
N
−
1, and the OFDM signal in a
symbol period is expressed as
N
−
1
n
=
∑
x
(
t
)
X
(
n
)
exp
j
2
π
t
0
≤
t
≤
T
.
(1)
T
n
=
0
Sampling this waveform at intervals
∆
t
=
T
/
N
(sampling frequency
f
s
= 1/
∆
t
) yields
N
−
1
nk
∑
x
(
k
)
=
X
(
n
)
exp
j
2
π
k
=
0
1
,
N
−
1
.
(2)
N
n
=
0
So,
x
(
k
) and
X
(
n
) from a DFT pair. This means that the baseband OFDM waveform
can be obtained from IDFT of the
N
modulating symbols. To obtain a real waveform
in the time domain, the complex symbol series
X
{
X
(1),
X
(2),
…
,
X
(
N
−
1)} is ex-
tended to the negative frequencies to give a new series,
Y
(
n
), of length
N
2
2
N
that is
conjugate-symmetrical:
X
(
n
)
0
≤
n
≤
N
−
1
Y
(
n
)
=
.
(3)
∗
X
(
N
−
n
−
1
N
≤
n
≤
N
−
1
2
2
