**6. References**


The performance of the Wavelet Transform based speech scrambling system was examined on actual " **Arabic Speech Signals** " , and the results showed that there was no residual intelligibility in the scrambled speech signal. The descrambled speech signal at receiver was exactly identical to the original applied speech waveform. Hence it provides the high security scrambled speech signal and the reconstructed signal was perfect . Some interesting

a. It is clear that (SNRs & SEGSNRs) give small values at any decomposition level, while (SNRd & SEGSNRd), give large values. As the level decreases the system performs better. The absolute low values of distance measures does not necessarily mean a perceptually poor assessments. The distance measures (SNR and SEGSNR) for scrambled/descrambled speech, can in some cases, be used for design purposes as a

b. The spectrogram is used because it is a powerful tool that allows us to see what's happening in the frequency and time domains all at once. Thus we can easily see the theory at work here by observing the original signal, it's scrambled version, and the descrambled version. Note that on the scrambled plot it is observed that the order of the frequencies has changed. And, as expected the descrambled version has been correctly

c. An evaluation of the speech scrambling system with different power levels of the additive white Gaussian noise was tested. The results proved that as the signal to noise ratio increases, the correspondence between original and descrambled speech increases. Hence, it can be concluded that, the WT algorithm can be implemented to scramble and

d. For real time speech scrambling it is recommended to use a wavelet with a small number of order at a reasonable decomposition level (level **3** decomposition or less), because the number of coefficients required to represent a given signal increases with the level of decomposition (higher wavelet decompositions requires more computation time, which should be minimized for real time speech scrambling) and with the large

Bopardikar, A. S. (1995). Speech Encryption Using Wavelet Packets. Indian Institute Of

DeelRe, E.; Fantacci, R. & Maffucci, D. (1989). A New Speech Signal Scrambling Method For

Gersho, A. & Steele, R. (1984). Encryption of Analog Signals a Perspective. IEEE Journal on

Goldburg, B.; Dawson, E. & Sridharan, S. (1991). The Automated Cryptanalysis Of Analog

Journal On Selected Areas in Communications, Vol.7, No.4.

Selected Areas in Communications, Vol. SAC-2, No.3

Secure Communications: Theory, Implementation, And Security Evaluation. IEEE

Speech Scramblers. Advances in Cryptology: Proceeding of EUROCRYPT'91, New

relative number of intelligibility loss or speech quality.

**5. Conclusion** 

points can be mentioned here:

decoded to its original form.

number of order.

Science.

York: Springer Verlag.

**6. References** 

descramble speech with high efficiency.


**4** 

*Singapore* 

**Wavelet Denoising** 

Guomin Luo and Daming Zhang *Nanyang Technological University* 

( ) *x* and an added

Removing noise from signals is possible only if some prior information is available. The information is employed by different estimators to recover the signal and reduce noise. Most noises in one-dimensional transient signal follow Gaussian distribution. The Bayes estimator minimizes the expected risk to get the optimal estimation. The minimax estimator uses a simple model for estimation. They are the most popular estimators in noise estimation.

No matter which estimator is used, the risk should be as small as possible. Donoho and Johnstone have made a breakthrough by proving that thresholding estimator has a small risk which is close to the lower bound. Thereafter, threshold estimation was studied extensively and has been improved by more and more researchers. Besides the universal threshold, some other thresholds, for example SURE threshold and minimax threshold, are also widely applied.

In wavelet denoising, the thresholding algorithm is usually used in orthogonal decompositions: multi-resolution analysis and wavelet packet transform. Wavelet thresholding faces some questions in its application, for example, the selection of hard or soft threshold, fixed or level-dependent threshold. Proper selection of those items helps

Besides the influence of thresholding, the influence of wavelets is also an important factor. In most applications, the wavelet transform uses a few non-zero coefficients to describe a signal or function. Producing only a few non-zero coefficients is crucial in noise removal and reducing computing complexity. Choosing a wavelet with optimum design to produce

The output acquired by sensing devices, for example transformer and sensor, is a measurement of analogue input signal *f* ( ) *x* . The output can be modelled as in (1). The

noise [ ] *W n* . The noise *W* contains various types of interferences, for instance, the radio frequency interferences from communication systems. It also includes the noises induced by measurement devices, such as electronic noises from oscilloscope and transmission errors. In most cases, the noise *W* is modelled by a random vector that often follows Gaussian

more wavelet coefficients close to zero is crucial in some applications.

output *X n*[ ] is composed by a filtered *f* ( ) *x* with the sensor responses

**1. Introduction** 

generating a better estimation.

**2. Noise estimation** 

distribution.

Yuan, Z. (2003). The Weighted Sum of The Line Spectrum Pair for Noisy Speech. M.Sc. Thesis, Department of Electrical and Communications Engineering, Helsinki University of Technology.
