Data Hiding in Digital Audio by Frequency Domain Dithering - Computer Network Security - page 390

N B

J =

2

− L D

. (14)

m

2

With the proposed technique, it is possible to embed several hundred bits into a single
segment lasting 20~30ms. For a given embedding capacity, the higher the sampling
frequency hence the bandwidth is, the shorter the required frame length. For high
fidelity music, the frame length can be very short so that the effect of data hiding on
sound quality is small.
Watermarks are usually embedded into a number of frames in the host audio.
These frames are organized into groups, and a chained structure is use to avoid
lengthy searches. The synchronization pilot was only inserted into the first frame of
each group with position information of the next frame contained in the embedded
data. The band assigned to the pilot was thus used to carry a pointer for the subse-
quent frame. Choosing the minimum spacing between frames as 32 N 2 where N 2 =
1024, a total of 20 candidate frames were identified in a segment of Radetsky March
lasting 23.77s, with f s = 44.1 kHz, 16 bits per sample, and embedding bandwidth w =
W /4. This resulted in a payload of more than 3,800 bits when using QAM, that is,
more that 540 ASCII characters, or nearly 25 characters per second.
The embedding induced distortion is a function of the quantization step

∆ . Fig.4

shows waveforms of a signal frame before and after embedding, with ∆ = max(| C n |)/8,

where max(| C n |) is obtained from a representative signal section. The value should

be included in the key. The two waveforms are hardly distinguishable. The difference
between them, very close to the horizontal axis, is also shown. Table 1 presents SNR
of the marked audio frame from Radetsky March with different quantization steps.

∆

0.4

Two waveforms almost overlap

0.2

0

-0.2

-0.4

-0.01 0 0.01 0.02 0.03

Tim e in s ec

Fig. 4. Waveforms of a signal frame before and after embedding, and their difference

Signal-to-noise ratios of the entire music, as a metric to assess imperceptibility, are
listed in Table 2. The largest quantization step was used in this experiment, (complete
replacement of the spectral lines within the embedding band). In the table, f s is the
sampling frequency, N q number of bits per sample, T length of the music, N f number
of embedded frames, and N b the total number of embedded bits. Even with the largest