Parameters Analyses

The control parameters of the echo data hiding techniques influence the percentage of watermark survival very much. Based on the hypotheses made in Chapter 2, the tests with various combinations of control

parameters (magnitude, watermark-embedding rate, delay times) are made in series on the simulation system. The watermark data used in the experiments are random generated in each test.

3.2.1 Parameter Ranges

First, the control parameter magnitude (A) was examined. The assigned value of A varies from 0.1 to 0.9, with step 0.1. Several fixed value of other parameters are given for the tests. In Fig. 25, the change of recovery accuracy rate generated from the varying magnitudes is shown, where the Wps was assigned as fixed values 2, 4 and 8, and the results shown are the average values of several different delay distance 0.3, 0.4 and 0.5msec, while a fixed d0=0.8msec was given.

Let us recall Hyporeport 1, which is about varied magnitudes, at the end of Chapter Two. In Fig. 25, an overall trend of the experimental results is the recovery accuracy rate decreases as the echo magnitude decreases, comparison of audio files

0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

echo magnitude

recovery accuracy rate

cello concerto kanon piano reading violin

Fig. 24 The recovery accuracy rate of different audio pieces A=0.1~0.9, step 0.1; Wps=2; d0=0.8msec; d1=1.2msec

0.4 0.5 0.6 0.7 0.8 0.9 1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

magnitude of echo

recovery accuracy rate

Wps=2 Wps=4 Wps=8

Fig. 25 Watermark recovery accuracy rate related to varying magnitudes A=0.1~0.9, step 0.1; Wps=2, 4, 8; d0=0.8msec; d1=1.1, 1.2, 1.3msec

which verified what the hyporeport said. The decrease of accuracy rate is not very obvious when the echo magnitude is large (in the range between 0.7 and 0.9).

This effect shows there is no need to assign a very large magnitude, so assigning A as high as 0.7 or 0.8 is quite enough. Since the acceptable recovery rate is defined as 0.75 (70% correction), the smallest allowable magnitude is approximately 0.3, as shows in Fig. 25. The echo with even smaller magnitude may not be correctly extracted.

From the experimental result, assigning the magnitude a value between 0.3 and 0.8 is recommended in the echo data hiding system.

Second, the watermark-embedding rate (Wps) was examined. A sequence of values, 2, 4, 8, … 256, was assigned for the tests of watermark-embedding rate.

Several specified values of magnitudes and delay times were assigned. The change of recovery accuracy rate with varying Wps is examined with A=0.75 and 0.65, and with d0=0.8msec, d1=1.2msec. Hyporeport 2 in Chapter 2

stated that the recovery accuracy rate decreases as the watermark-embedding rate increases. The decreasing tendency of the accuracy rate as the Wps increased is clearly shown in Fig. 26. The decrease of the recovery accuracy rate is more obvious when higher Wps is given.

This effect implies when low Wps (in the range between 2 and 32) is assigned, there would not be as large difference between the recovery results. From the test results shown in Fig. 26, the assignment of the watermark-embedding rate is suggested to be in the scope from 2 to 128, which has an accuracy rate better than the predefined acceptable recovery accuracy rate.

Third, the influence from assigning varying delay times is considered. Several different distances of the smaller delay (d0) from the original were tested. The distance between d0 and the zero point of time domain (|d0–0|) was given values that varied from 0.1 to 0.8msec.

Fig. 27 shows the experimental results of varying delay distances from the original signal. The distance between

0.4 0.5 0.6 0.7 0.8 0.9 1

2 4 8 16 32 64 128 256 512

watermark-embedding rate (per second)

recovery accuracy rate

average maximum minimum

Fig. 26 Relationship between the recovery accuracy rate and varying watermark-embedding rate A=0.65, 0.75; Wps=2~512, step 2 time; d0=0.8msec; d1=1.2msec

0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 0.3 0.5 0.7 0.9

delay0 (msec)

recovery accuracy rate

A=0.8; Wps=4 A=0.8; Wps=16 A=0.5; Wps=4 A=0.5; Wps=16

Fig. 27 Relationship between value of d0 (the smaller delay) and the accuracy rate A=0.5, 0.8; Wps=4, 16; d0=0.1~0.9msec, step 0.2msec; delay distance= 0.5msec

the delays was fixed at 0.5msec, that is |d1–d0|=0.5msec.

The magnitudes of the echoes were fixed at A=0.8 and 0.5, and the watermark-embedding rates were assigned as Wps=4 and 16 in these experiments. The trend of increasing the recovery accuracy rate as the length between the original and the smaller delay increases can be easily told from Fig. 27. This effect is based on the autocorrelation characteristics of the audio as discussed in prior chapter. Based on the experimental results, to achieve the acceptable recovery rate, the offset of smaller delay needs to be at least 0.6msec from the original.

Besides the influences of distance between the original signal and the echo signal with smaller delay, the influences of distance between the delays also need to be considered. Based on the experimental results in the prior section, value of d0 was assigned as 0.8msec while d1 was given values varied from 0.6 to 1.6msec, with step size 0.1msec. The other control parameters are given as fixed values, 0.75 and 0.6 for the magnitude, and the watermark-embedding rate is two in the tests with varying delay distance. While Hyporeport 4 implies the accuracy rate of recovery would increase as the distance between delays increase, the experimental results match this assumption. As Fig. 28 illustrated, the accuracy rate increases obviously with the increasing delay distance from |d1–d0|=0.1 to 0.4msec. The delay distance does not make as much difference on the recovery rate when the distance is larger then 0.4msec. To reach the acceptable

recovery rate, 0.75, the delay distance should be kept larger than 0.3msec based on the experimental results.

In this section, varied values of the control parameters are examined to find out the best suit range for the control parameters assignment. For echo magnitude, the value range from 0.3 to 0.8 is suggested;

and for watermark embedding rate, the scope of 2 to 128 is recommended. The delay values should be at least 0.6msec away from the original while keeping a distance larger than 0.3msec between each other.

4.2.2 Correlation of Parameters

There exist some correlations between the control parameters under the satisfaction of acceptable recovery accuracy rate. Three of the correlations are examined;

including the relationship between echo magnitude and watermark embedding rate based on Hyporeport 5; the relationship between magnitude and delay distance of echo signals based on Hyporeport 6; and the relationship between watermark embedding rate and delay distance based on Hyporeport 7. In the experiments, these control parameters are assigned values in the suggested proper range, and the selected parameter combinations have the accuracy rates of approximately 0.8, which is a little larger than the predefined acceptable recovery accuracy rate to avoid the influence of variance between various audio signals.

0.4 0.5 0.6 0.7 0.8 0.9 1

-0.2 -0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

delay distance

recovery accuracy rate

average maximum minimum

Fig. 28 Relationship between the delay distance and the recovery accuracy rate A=0.75, 0.6; Wps=2; d0=0.8msec; d1=0.6~1.6msec, step 0.1msec, but d1≠0.8msec.

The relationship of the magnitude and the watermark-embedding rate was considered under the range of 0.3≤A≤0.8 and 2≤Wps≤128, and the delay distance was given as 0.3, 0.5 and 0.7msec. To achieve the acceptable recovery accuracy rate, the requirement of A and Wps pairs were determined, as Fig. 29 illustrated.

When the Wps was given as 128, the magnitude had to be larger then 0.7 to achieve the accuracy rate 0.8; while the magnitude can be as small as 0.4 when the Wps is 2. This result verified what Hyporeport 5 said, when assigning a higher watermark embedding rate, the magnitude of echoes needs to be larger. This experimental result also gives a reference for parameter assignment, where the minimum magnitude for each watermark embedding rate or the maximum watermark-embedding rate for each magnitude is shown.

There also exist some tradeoffs between the delay distance and the echo magnitude, and between the delay

distance and the watermark embedding rate under certain performance requirements while the recovery accuracy rate is larger than 0.8. In the experiments, the magnitudes were assigned in the range 0.3≤A≤0.8, and the embedding rates were given in the range 2≤Wps≤128, while the delay distance varies from 0.1 to 1msec.

The experimental results are shown in Fig. 30 and Fig. 31. The trend of the curves is very clear in the correlation tests of the magnitude and the delay distance, the former can be smaller as the latter is increased while keeping the recovery accuracy rate at the same level, which verifies Hyporeport 6. The relationship between the watermark embedding rate and the delay distance of echo signals is also obvious, although the curve is not as linear as the previous experiment. The flat stages of the curve occur because the Wps were assigned as a geometric series, where the appearance of not enough precision can be improved by giving values of the Wps as

0.3 0.4 0.5 0.6 0.7 0.8

2 4 8 16 32 64 128

watermark-embedding rate

magnitude

Fig. 29 Tradeoff between magnitude and watermark-embedding rate

A=0.3~0.8, step 0.1; Wps=2~128, step 2 time; d0=0.8msec, d1=1.3, 1.5msec, and d0=1msec, d1=1.3, 1.5msec.

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1 0.3 0.5 0.7 1

delay distance (msec)

magnitude

Wps=2 Wps=4

Fig. 30 Tradeoff between the delay distance and the magnitude of echo A=0.3~0.8, step 0.1; Wps=2, 4; d0=0.8msec, d1=0.9, 1.1, 1.3, 1.5, 1.8msec

an arithmetic progression. Based on the experimental results, the watermark-embedding rate can be larger when the delay distance is longer under the same recovery accuracy rate, and Hyporeport 7 is verified. The results in Fig. 30 and Fig. 31 also give references for the parameter assignments.

These experimental results make the parameter assignment easier. The parameter assignment of a system can be done when considering the recovery accuracy rate, information transmission rate. The audio quality also needs to be considered. An echo magnitude as 0.7 is usually allowed when the largest delay value is smaller than 1.3msec, and a magnitude near 0.5 is usually allowed when the delay value is near 2.5msec.

Although a tradeoff between the recovery accuracy rate and the number of digit for watermark representation must be made, the multiple-bits echo data hiding system does work.