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Reduce noise in underwater for acoustic signal using different technology. There are some specified filter Wiener filter, Adaptive filter, and Wavelet Thresholding.Underwater acoustic telemetry exists in applications such as data harvesting for environmental monitoring, communication with and between manned and unmanned underwater vehicles, transmission of diver speech, etc. Reduce noise in underwater for the acoustic signal.
• Sound propagation losses
• Self-noise and ambient noise, SNR
Acoustic communications form an active field of research with significant challenges to overcome, especially in horizontal, shallow-water channels. Because of the activities of people in the ocean are expanded, the field of underwater acoustics has been extensively developed in a variety of applications including acoustic communication, the detection and location of surface and subsurface objects, depth sounders, and sub-bottom profiling for seismic exploration.
A noise removal algorithm based on short-time Wiener filtering is described. An analysis of the performance of the filter in terms of processing gain, mean square error, and signal distortion is presented. Noise hampers sonar data collection and related processing of the data to extract information since many of the signals of interest are of short duration and of relatively low energy. Data from passive sonar is generally accompanied by ambient noise arising from shipping traffic, marine life, wave motion, moving and cracking ice (in the Arctic), and numerous other sources.
Where x (n) is the received noise-corrupted signal, s (n) is the uncorrupted signal, and ? (n) is the additive noise.
Although the signal is not usually stationary over a long observation time, for a short time interval we can write Rx (I) = Rs (I) + R? (I)
The estimate of the signal is a classical problem in statistical signal processing, and the vector of optimal FIR (Wiener) filter coefficients he the solution to the Wiener-Hopf equation Rx h = Rs.
Where Rx is the correlation matrix for the observed noisy signal, and rs is a vector of terms from the correlation function &R (l) of the uncorrupted signal.
The pre-whitened data is segmented into blocks where an estimate of the local correlation function Rs (I) is formed for each segment.
Optimal filtering is then performed for each segment using a Wiener filter designed for the segment and the data is processed by the inverse filter to undo the effects of the pre-whitening.
The data is first segmented and filtered and the resulting frames are weighted by a triangular window. The data is then re-segmented using frames shifted by half of the frame length, filtered again and weighted by a triangular window.
The two weighted sets of data are then added to produce the final result and “minimize any effects that may occur at the boundaries between frames.
The figure depicts the linear filtering of a signal in additive noise and indicates the two portions of the output: ys (n) the result of processing the signal alone, and y? (n) the part due to processing the noise alone, which can be thought of as the residual noise left after processing.
A measure of signal distortion introduced by the filter can be defined as
The evaluation is performed on are representative real data set of underwater acoustic records. Rationales used to process the proposed evaluation are mean squared error, global signal-to-noise ratio (SNR), segmental SNR and mean squared spectral error. These filters are generally designed by a calculation which involves the signal autocorrelation estimation, a difficult task in case of low SNR or presence of non-stationary components. Musical noise is a perceptual phenomenon that occurs when isolated peaks remain in the time-frequency representation after processing with spectral subtraction algorithm 
1. Observation model
The observation represents N data samples, it is noted z[n], noise is noted ?[n] and a signal of interest is noted s[n]. So, for each sample n = 0 … N – 1, we have Z[n] = s[n] + ?[n] As some of the proposed methods proceed observation into the time-frequency plane, it is necessary to briefly recall some useful properties. In this case, the short-time Fourier transform (STFT) of the observed signal is defined by Where w is a K-length time window, k = 0 … K – 1 and l = 0 … L – 1 are respectively the frequency and time indexes. Frames overlap is defined by N01.
2. Statistical Assumptions for Noise
Noise is considered as a locally centered WSS Gaussian process. The assumption of Gaussian distribution is motivated by the similitude observed between the sea noise distribution and its theoretical fitting Gaussian distribution. However, note that sea noise is colored so its power spectral density (PSD) is not constant, especially in low frequencies domain.
2) Time-Frequency Domain
On each frequency channel k = 0 … K – 1, the noise Fourier coefficients ? [k, l] are circular symmetric complex Gaussian random variables, independent of S [k, l]. Thus the noise is considered stationary and its variance does not depend upon a time:
The latest noise reducing methods have been mainly designed to reduce this phenomenon while preserving or even improving the signal elements detection on time-frequency representation (TFR).
1. Wiener Filtering (WF)
In 1940, Norbert Wiener built a finite impulse response filter (FIR) w [n] to estimate the signal of interest s[n] from its noisy observation z[n]. This filter is built to minimize the mean squared error between the signal of interest and its estimation. It is shown that the coefficients of this filter are calculated by Where, r denotes the autocorrelation of s[n] and R the covariance matrix of z[n]. R is a symmetric positive semi-definite matrix, and therefore invertible as long as z[n] variance is nonzero.
2. Wavelet Thresholding (WT)
The sixth one is the famous Donoho’s wavelet thresholding method, operating to remove the noisy part from the wavelet coefficients. The first step consists in computing the discrete wavelet transform (DWT) of the signal with the multi-resolution algorithm. To do so, a filters bank is built from a given mother wavelet ?(t) such as
Where j is the scale parameter and k is the shift parameter. For the evaluation, a 6 order Daubechies wavelet is used to compute the DWT. The second step consists in thresholding, in the wavelet domain, by shrinking the coefficients wj,k with the soft thresholding method described in :
Where N is the number of samples and sj the noise standard deviation at scale j. The method MDF produces slightly better performances at low SNR and on colored noise.
The authors S.S.Murugan, et studied the real-time data collected from the Bay of Bengal at Chennai by implementing Welch, Barlett and Blackman estimation methods and improved the maximum Signal to Noise Ratio to 42-51 dB. The sources include geological disturbances, non-linear wave interaction, turbulent wind stress on the sea surface, shipping, distant storms, seismic prospecting, marine animals, breaking waves, spray, rain, hail impacts and turbulence. A direct connection between wind force and the level of ambient noise is observed for a frequency range of 500 Hz to 25 kHz. Noise level spectrum is summarized. The work on spectra and sources of ambient noise in the ocean observed a decrease in wind/sea state dependency of underwater ambient noise below 500 Hz.
Spectral estimation plays an important role in the signal detection and tracking. The applications of spectral estimation include harmonic analysis and prediction, time series extrapolation and interpolation, spectral smoothing, bandwidth compression, beamforming and direction finding. Spectral estimation is based on the idea of estimating the autocorrelation sequence of a random process from a set of measured data and taking the Fourier to transform to find the estimate of the power spectrum.
1. Bartlett Method
Bartlett method is also known as periodogram averaging. In this method, the input sequence x(n) of length N is partitioned into K nonoverlapping sequences of length L such that N= KL. The Bartlett estimate is given by:
2. Welch Method
Welch method is also known as modified periodogram. Welch proposed two modifications to Bartlett’s method. The first is to allow the sequence xi(n) to overlap and the second is to allow a data window w(n) to be applied to each sequence. The estimate produced by Welch method is given by:
3. Blackman-Tukey Method
The black man-Tukey method is known as smoothing of periodogram. This estimate smoothes the periodogram by convolving with the Fourier transform of the autocorrelation window [W (e j? ) ]. The Blackman-Tukey spectrum is given by:
4. Adaptive Filtering Algorithm
Many computationally efficient algorithms for adaptive filtering have been developed. They are based on either a statistical approach, such as Least-Mean-Square (LMS) algorithm, or a deterministic approach, such as Recursive Least-Squares (RLS) algorithm. Adaptive noise cancellation techniques are employed to mitigate the unwanted noise effects.
4.1 LMS Algorithm
LMS algorithm is a member of stochastic gradient algorithms. The recursive relation for updating the tap-weight vector is given by: W (n +1) = w (n) + µx (n) e * (n)
Here x (n) is the input to the filter, e (n) is the error signal and µ is the step-size. At each iteration, this algorithm requires knowledge of the most recent values u (n), d (n) and w? (n).
4.2 NLMS Algorithm
The term normalized is due to the adjustment applied to the tap-weight vector at iteration n +1 is “normalized” with respect to the squared Euclidean norm of the tap input vector x(n) at iteration n. NLMS differs from LMS by the way in which the weight controller is mechanized. The recursive relation for updating the tap-weight vector is given by:
The Recursive Least Squares (RLS) adaptive filter is an algorithm which recursively finds the filter coefficients that minimize a weighted linear least squares cost function relating to the input signals. This is in contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity, and potentially poor tracking performance. RLS algorithm is defined by following equations. Initialize the algorithm by setting: w? (0) = 0 P (0) =d -1 I Where, d is a constant For each instant of time, n = 1, 2, 3… Compute
To minimize the effect due to the wind, various adaptive algorithms are processed and compared for achieving maximum SNR. RLS is found to be better when compared with other algorithms. Using RLS, SNR of about 42 –51 dB is achieved, which is comparatively very high.
The authors Yen-Hsiang Chen et al  implemented a real-time adaptive Wiener filter with two microphones is implemented to reduce noisy speech when noise signals and desired speech are incoming simultaneously. The performance of the proposed design is measured by as much as 20dB noise reduction, and the proposed adaptive Wiener matrix update speed achieves a 28.6 ms/frame, with a matrix size of 200. A real-time adaptive Wiener filter for non-Stationary noise cancellation. It can efficiently evaluate the performance and cost of the individual components of noise reduction. The speech recognition in an in-vehicle environment needs a non-stationary noise cancellation to eliminate the background noise.
ADAPTIVE WIENER FILTERS
The goal of the Wiener filter is to filter out noise that has corrupted a signal by statistical means. As described in Equation (1), a microphone signal y (an M-dimensional vector) is filtered by the Wiener filter W (an M*M filter matrix) and the output z (an M-dimensional vector) has to estimate the desired signal d with some residual errors. Equation (1) shows that when z = d then e = 0. This means that when e = 0, z is the estimated value of, therefore when the desired signal comes with noise (white or colored), a selected W matrix is available for estimating the desired signal.
Microphone 2 acts as a speech and noise input or primary. Microphones 1 and 2 record the desired speech and unwanted speech while desired speech is mainly from microphone 2 and an unwanted speech or noise source is mainly from microphone 1. There are two main processing units in the proposed design which are named correlation analysis and the Wiener filter. Auto-correlation is a special case of cross-correlation which computes a signal with itself, it generates 2N -1 values. And permutes into an N * N matrix. The auto-correlation results are generated in Toeplitz matrix format for future processing.
The matrix subtraction unit subtracts every element from two matrices independently and forwards the results to the matrix multiplication. The matrix multiplication and the matrix-vector multiplication are similar processing units, the difference between two units is that the matrix-vector multiplication performs a matrix multiplication to an N*1 matrix.
Because of the activities of people in the ocean are expanded, the field of underwater acoustics has been extensively developed in a variety of applications including acoustic communication, the detection and location of surface and subsurface objects, depth sounders, and sub-bottom profiling for seismic exploration. Until now on, an acoustic wave is still the optimum medium for signal transmission in the ocean. Thus, identification and recognition of acoustic signals have become as the primary subject of underwater techniques. Underwater acoustic signals are affected by ocean condition and ambient noise during the transmission. The sources of ambient noise are both natural and human-made, with different sources exhibiting different directional and spectral characteristics. Therefore, before recognizing the received acoustic signals, it is necessary to remove the noise so as to keep the important signal features as much as possible.
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