IJECET Wavelet Denoising of Underwater Signals

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online), Volume 5, Issue 4, April (2014), pp. 57-64 © IAEME
57
WAVELET BASED DENOISING TECHNIQUE FOR UNDERWATER SIGNAL
AFFECTED BY WIND DRIVEN AMBIENT NOISE
Ramesh D1
, Ranjani G 2
1
M.Tech Student and 2
Assistant Professor
Department of Telecommunication Engineering, R.V. College of Engineering, Bangalore, INDIA
ABSTRACT
Underwater communication is afast growing technique in the field of communication. It is
used to communicate data between the underwater equipments. EM signals will undergo high
attenuation in the seabecause of their high frequency. Sound waves will propagate very well in
ocean. Underwater communication is a challenging issue since the communication channel contains
various disturbances in the form of noise. The noise due to wind plays a vital role in underwater
communication. The main objective of this paper is to denoise the low frequency underwater signals
affected by wind noise. A mathematical model is developed for wavelet based denoising of a signal.
This denoising method is based on the universal threshold value estimation method. This method
reduces the wind driven ambient noise content in the noisy signal and improves the SNR of the
signal.
Keywords: Ambient Noise, Discrete Wavelet Transform (DWT), Thresholding, RMSE, SNR.
I. INTRODUCTION
Signal transmission in ocean using water as a channel is a challenging process due to the
effect of attenuation, spreading, reverberation, absorption etc., apart from the contribution due to
ambient noises. Ambient noises in sea are of two types namely manmade (shipping, aircraft over the
sea, motor on boat, etc.) and natural (rain, wind, marine fishes, seismic, etc.). The ambient noises
contribute more effect on reducing the quality of acoustic signal. In this project the concentration is
on Denoising the effect due to wind on underwater acoustic signal using the wavelet transform.
Ambient ocean noise changes over time and is therefore non-stationary. However the
variability of the predominant sources (wind speed and shipping density) change slowly over the
course of hours or longer. Similarly the properties of the ocean itself that affect propagation (such as
INTERNATIONAL JOURNAL OF ELECTRONICS AND
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ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 5, Issue 4, April (2014), pp. 57-64
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58
temperature and density) change even more slowly. So for the purpose of analyzing data segments on
the order of a few seconds, the ambient ocean noise can be assumed to be stationary.
Wavelet analysis provides a unified framework to a number of techniques that are applied in
various research areas including mathematics, computer imaging and geophysics. In signal
processing wavelet-based techniques can be found in applications such as multi-resolution
processing, signal compression, sub band coding and noise removal.
For the analysis and detection of sound signals Fourier transform is mostly used. Although
this transform is extremely useful and well established, it is not efficient in analyzing the short-term
transient sound behavior. Various short-time Fourier transforms (STFT), having a variety of
“windows” with varying length, have been developed to address this problem. An alternative to the
Fourier transform and STFT with better time-frequency localization is wavelet transform [1]. This
paper explores the use of the wavelet transform in signal detection against wind driven ambient
noise.
In this paper, an interval-dependent thresholding method was used to remove the noise from
the low frequencysignals. Root Mean Square Error (RMSE) calculated to evaluate the performance
of the wavelet based interval-dependent thresholding method for denoising low frequency signals. It
also was realized a comparative study to show the effectiveness of the intervaldependent
thresholding method with hard and soft thresholding techniques for different SNR values.
II. LITERATURE
Different adaptive filter algorithms are analyzed in detail to eliminate the effect due
to wind on the signal transmitted and signal to noise ratio is calculated [1]. The SNR obtained for
various types of adaptive algorithms are analyzed and tabulated for different wind speed.
The methodology of denoising the partial discharge signals shows that the proposed
Denoising method results are better when compared to other approaches like FFT, by evaluating
Signal to noise ratio, Cross correlation coefficient, Pulse amplitude distortion, Mean square error,
and Reduction in noise level [2].Different basis functions can be used to decompose the various
frequency bands. These basis functions are called as mother wavelets. These mother wavelets for
each wavelet family differ from each other by scaling and shifting parameters. Thresholding is used
in wavelet domain to smooth out or to remove some coefficients of wavelet transform sub-signals of
the measured signal [3].
The ambient noise levels are significantly affected by the snapping shrimp sound, when the
bottom seawater temperature increases and the wind speed decreases. However, they are not
exceptively almost affected by the snapping shrimp sound when the wind speed decreases at low
seawater temperatures (<10 °C). In diurnal variation, the ambient noise levels are also significantly
affected by the snapping shrimp sound in the morning and night time zones. This study shows that
the activity of the snapping shrimp affecting the variation in ambient noise level in shallow water can
be related to the wind speed as well as the seawater temperature. This study also shows that the
snapping shrimp in diurnal activity can be more active in the morning and night time zones [4].
Winds are the primary driver of large-scale ocean currents. They are responsible for the
formation of the Gulf Stream. Improved understanding of the global pattern of wind is needed to
improve weather and climate forecasting. Information on wind over the ocean helps meteorologists,
oceanographers, and climatologists. Ambient noise data were collected for the period of six months
in the shallow water of Arabian Sea. Data’s were collected for different wind speed ranges between
0.5 m/s to 7 m/s and the analysis were performed for frequencies ranging from 500 Hz to 7 KHz [5].
The relative spectral energy distribution of sea noise is presented for a number of wind speeds.
Linear relationship between the sea noise spectrum levels and the wind speed were found for the
entire frequency range.

59
In this proposed method we systematically utilizing the above mentioned research to examine
the frequency signal of 7000Hz which is affected by noise, can be denoised effectively using the
proposed algorithm.
Theproposed system will not only denoise the signal but it also gives the smoothness in the
signal so that much of information is not lost.
III. METHODOLOGY
The presented method is based on decomposing the signal into four levels of wavelet
transform by using different wavelets and determining a threshold by universal threshold method as
shown in the figure 1.
Figure 1: Denoising Process
DWT provides the sufficient information, both for analysis and synthesis and reduce the
computation time sufficiently. It analyze the signal at different frequency bands with different
resolutions, decompose the signal into a coarse approximation and detail information.
The general procedure for wavelet based de-noising [3] is
1) Decomposition
Choose a wavelet, choose a level N. Compute the wavelet decomposition of the noisy signal
at level N
2) Threshold detailed coefficient
For each level from 1 to N, select a threshold and apply Hard/Soft for detailed noisy
coefficient to get the modified detailed coefficient.
3) Reconstruction
Compute wavelet reconstruction using the original approximation coefficient of level N &
modified detailed coefficient of levels 1 to N.
Algorithm:
The algorithm of the wavelet based interval-dependent denoising is as follows:
Step1: Decomposing of the noisy signal using the discrete wavelet transform into detailed and
approximate components.
Step 2: Noise variance at each wavelet scale is calculated using Eq. 2.
Step 3: The threshold is calculated at each level using Eq.1
Step 4: Hard and soft threshold values are calculated using Interval-dependent thresholding method
of in the different Intervals by using Eq. 3 or 4.
Step 5: The original signal is reconstructed from the modified coefficients using the inverse wavelet
transform.

60
3.1. Noisy Signal
The noisy signal is generated using MATLAB. The AWGN noise is added to the sine signal.
The noisy signal used for the analysis is as shown in figure 1.
Figure 2: Noisy signal
3.2: Discrete Wavelet Transform
Fourier transform gives information about frequency content of signal, but it does not show at
what times frequency components occur. It is the reason why we use Short term Fourier transform
and wavelet transform for analysis of signals like audio or speech.
Wavelet transform has advantage over Short term Fourier transform because it analyzes the
signal at different frequency with different resolutions. High frequency components have good
temporal localization, but frequency resolution is poor. Low frequency components have good
frequency resolution, but they are not localized in time well. This approach is called multiresolution
analysis and it makes sense when signal has high frequency components for short durations and low
frequency components for long durations. This approach has certain similarities with Bark-scale of
human auditory system: human ear has better frequency resolution at low frequencies and lower
frequency resolution at high frequencies.
The discretized continuous wavelet transform enables the computation of the continuous
wavelet transform by computers, but it is highly redundant and requires significant computation time
and resources. Discrete wavelet transform (DWT) provides analysis and synthesis of original signal
with significant reduction in the computation time. Decomposition of the signal is obtained by
passing time domain signal through half band low pass and high pass filters. Filtering the signal is
equivalent to convolution of signal with impulse response of filter.
The decomposed signal using DWT will yield detailed and approximate coefficients as
shown in figure 3.
Figure 3: Wavelet Coefficients
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10
-3
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time
Amplitude
Noisy signal
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-5
-4
-3
-2
-1
0
1
2
3
4
5
Data number
Amplitude
Wavelet coefficients Approx-Low , Detailed- High
level 4 - approx
level 4- detailed
level 3- detailed
level 2- detailed
level 1- detailed

61
3.3: Thresholding
The noisy signal decomposed with the detail coefficients and the approximation coefficients.
Low-frequency components are shown with large coefficients and highfrequency components are
shown with small coefficients. Wavelet coefficients that is smaller than the threshold value is
removed. As a result, the original signal is obtained from the noisy signal. Method in this article, the
threshold values are obtained separately for each level of wavelet transformation. Because, high-
frequency and lowfrequency parts of the signals have different features such as mean value and
standard deviation. Therefore intervaldependent threshold value is calculated separately for each
level and each interval is denoised.
The denoising method which is used for thresholding in wavelet domain has been proposed
by Donoho as a powerful method. The method is based on applying the wavelet transform of a signal
and passing it through a threshold. This threshold value is generated from any of the functions
namely ‘rigrsure’, ‘heursure’, ‘sqtwolog’, ‘minimaxi’ and universal. Threshold value using universal
threshold estimation [3] is given by
λ ൌ σ√2l‫ܰ݃݋‬ ..…………… (1)
The variance of noise (σ) is given by
σൌ
௠௘ௗ௜௔௡|௫|
଴.଺଻ସହ
………………(2)
where,
λ is the threshold value.
N is the length of the signal.
x is the noisy signal.
Types of Thresholding:
Hard and soft are the basic two types of thresholds
1) Hard Thresholding
Hard thresholding [3] is also called as gating. If a signal or a coefficient value is below the
threshold value (ߣ), it is set to zero. This allows retaining the sharp features of the signal. The hard
thresholding function given in Eqn (3)
݂௛ ൌ ൜
‫;ݔ‬ |‫|ݔ‬ ൐ ߣ
0; |‫|ݔ‬ ൑ ߣ
ൠ ………………. (3)
2) Soft Thresholding
In soft thresholding [3] the coefficients with magnitudes smaller than the threshold value (ߣ)
are set to zero, but the retained coefficients are also shrunk towards zero by the amount of the
threshold value in order to decrease the effect of noise assumed to corrupt all the wavelet
coefficients. The soft thresholding function given in Eqn (4)
݂௦ ൌ ൜
‫݊݃ݏ‬ሺ|‫|ݔ‬ െ ߣ; |‫|ݔ‬ ൐ ߣ
0; |‫|ݔ‬ ൑ ߣ
ൠ………... (4)

62
Figure 4: Wavelet Coefficient after hard thresholding
Figure 5: Wavelet Coefficients after soft thresholding
3.4: Reconstruction
The original signal is reconstructed from the modified coefficients using the inverse wavelet
transform.
The noisy signal using wavelet transform is decomposed into 4 levels. Then, thethreshold
value is determined separately for each level. The wavelet coefficients of the noise are eliminated.
The original signal is obtained from the retained coefficients. Figure 6 and 7 shows the reconstructed
signal using soft and hard thresholding. The most important feature of this method is to determine
the threshold for each level separately. This feature improves the performance of the algorithm.
Figure 6: Reconstruction using soft thresholding
Figure 7: Reconstruction using hard thresholding
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-5
-4
-3
-2
-1
0
1
2
3
4
5
Data Number
Amplitude
Wavelet coefficient after Hard Thrsholding
level 4 - approx
level 4- detailed
level 3- detailed
level 2- detailed
level 1- detailed
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-5
-4
-3
-2
-1
0
1
2
3
4
5
Data Number
Amplitude
Wavelet coefficient after Soft Thrsholding
level 4 - approx
level 4- detailed
level 3- detailed
level 2- detailed
level 1- detailed
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-1.5
-1
-0.5
0
0.5
1
1.5
Reconstructed signal using Soft thresholding
Data number
Amplitude
0 200 400 600 800 1000 1200 1400 1600 1800 2000
-1.5
-1
-0.5
0
0.5
1
1.5
Reconstructed signal using Hard thresholding
Data number
Amplitude

63
IV. RESULTS
In this proposed system, the 7000Hz sine wave is generated using MATLAB and then the
additive white gaussian noise (AWGN) is added to the generated sine wave.
The noisy signal is used of different SNR as 10 and 20 dB for haarwavelet is used for
analysis and the four level of decomposition is carried out. After the decomposition, the thresholding
is estimated for each level using universal thresholding method.
The wavelet coefficients are then passed through soft and hard thresholding and then the
signal is reconstructed using the modified wavelet coefficients.
Table 1: SNR & RMSE VALUES
The simulation results shows the improvement in SNR of the denoised signal hence the
algorithm is best suited for denoising of the signal for non-stationary signals.
V. CONCLUSION
Wavelet based denoising technique has been proposed with the modification in the threshold
estimation methods and the thresholding methods. This new method is used to denoise the signal
added with the wind driven ambient noises. This method results in the improvement in SNR of the
denoised signal. From the estimated RMSE values it can be concluded that, noise is reduced in the
denoised signal when comparing to the noisy signal. The analysis is carried out with thehaar wavelet
and it is found that the soft thresholding is best suited to increase the SNR.
REFERENCES
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Wavelet
type
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signal
Universal threshold
estimation method
Soft
Threshold
Hard
threshold
HAAR SNR(dB) 10 17.984198 17.984198
20 30.785163 30.785163
RMSE 10 0.393359 0.429902
20 0.224484 0.226839

64
[4] Byoung Nam Kim, Bok Kyoung Choi, Bong Chae Kim, SeomKyu Jung, Yosup Park, Yong
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