These noise and interference makesthe incorrect diag- nosis of the ECG signal [1-3]. So, theremoval of these noise and interference from the ECG signalhas become very crucial. Different types of digital filters (FIRand IIR) have been used to solve the problem [3-5]. However,it is difficult to apply these filters with fixed coefficients toreduce different types of noises, because the ECG sig- nal isknown as a non-stationary signal. Recently, adap- tive filteringhas Become effective and popular methods for processing andanalysis of the ECG signal [6-8]. It is well known thatadaptive filters with **least** **mean** **square** (LMS) **algorithm** showgood performance for process- ing and analysis of signal whichare non-stationary [1]. And in this study, we have usedadaptive LMS and nor- malized **least** **mean** **square** (NLMS)filter to denoise the ECG signal. We also have evaluated theirperformance. But it is shown that NLMS filter removes allspecified noise (mentioned above) more significantly.

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channel estimation methods have a common drawback of sensitivity to the scaling of random training signal. Thus, it is very hard to choose a proper learning rate to achieve a robust estimation performance. To solve this problem, we propose several improved **adaptive** sparse channel estimation methods using normalized LMS **algorithm** with different sparse penalties, which normalizes the power of input signal. Furthermore, Cramer-Rao lower bound of the proposed **adaptive** sparse channel estimator is derived based on prior information of channel taps' positions. Computer simulation results demonstrate the advantage of the proposed channel estimation methods in **mean** **square** error performance.

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Abstract- Acoustic Echo Cancellation (AEC) **algorithm** play a vital role in mobile communication systems, which control the step size by decreasing the estimated error while improving the convergence. Here, as it is investigated various **adaptive** filters named LMS, normalized LMS and Encumbered Constancy LMS (ECLMS) algorithms for a step size control method capable of slowly canceling acoustic echo resisting dual talk. The proposed method is an extension for the conventional AEC **algorithm** in which the step size has controlled by using a single **adaptive** filter. The proposed method uses two **adaptive** filter structures named as sub- **adaptive** filter (SADF) which controls the step size and the main **adaptive** filter (MADF) used for canceling the acoustic echo. Accordingly, the sub-**adaptive** filter can reduce the residual echo more rapidly than the main **adaptive** filter. The method applies the step size calculated using the normalized residual echo to the main **adaptive** filter and thereby rapidly and steadily reduces the acoustic echo. Simulations results have been shown that the proposed ECLMS performed superior to the LMS and NLMS even that of conventional **adaptive** filters in terms of convergence and estimated error.

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The power line interference (50/60 Hz) is the main source of noise in most of bio-electric signal. In this paper second order infinite impulse response (IIR) notch filter, **adaptive** notch filtering technique with LMS (**least** **mean** **square**) **algorithm** and Discrete Wavelet transform method has been proposed for the removal of power line interference from ECG signal. Different ECG signals from MIT/BIH arrhythmia database are used with added power-line interference noise which is common in ECG signal. The result is analyzed using MATLAB software. Basically two synthesis parameters MSE and SNR have been used. The prime aim of this paper is to adapt the discrete wavelet transform (DWT) to improve the ECG signal quality for better clinical diagnosis. The proposed method shows improvement in output SNR is 97.60%.

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High bit rates optical communication systems pose the challenge of their tolerance to linear and nonlinear fiber impairments. Digital filters in coherent optical receivers can be used to mitigate the chromatic dispersion entirely in the optical transmission system. In this paper, the **least** **mean** **square** **adaptive** filter has been developed for chromatic equalization in a 112-Gbit/s polarization division multiplexed quadrature phase shift keying coherent optical transmission system established on the VPIphotonics simulation platform. It is found that the chromatic dispersion equalization shows a better performance when a smaller step size is used. However, the smaller step size in **least** **mean** **square** filter will lead to a slower iterative operation to achieve the guaranteed convergence. In order to solve this contradiction, an **adaptive** filter employing variable-step-size **least** **mean** **square** **algorithm** is proposed to compensate the chromatic dispersion in the 112-Gbit/s coherent communication system. The variable-step-size **least** **mean** **square** filter could make a compromise and optimization between the chromatic dispersion equalization performance and the **algorithm** converging speed. Meanwhile, the required tap number and the converged tap weights distribution of the variable-step-size **least** **mean** **square** filter for a certain fiber chromatic dispersion are analyzed and discussed in the investigation of the filter feature.

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This article develops a new **adaptive** filter **algorithm** intended for use in active noise control systems where it is required to place gain or power constraints on the filter output to prevent overdriving the transducer, or to maintain a specified system power budget. When the frequency-domain version of the **least**-**mean**-**square** **algorithm** is used for the **adaptive** filter, this limiting can be done directly in the frequency domain, allowing the **adaptive** filter response to be reduced in frequency regions of constraint violation, with minimal effect at other frequencies. We present the development of a new **adaptive** filter **algorithm** that uses a penalty function formulation to place multiple constraints on the filter directly in the frequency domain. The new **algorithm** performs better than existing ones in terms of improved convergence rate and frequency-selective limiting.

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It is a Normalized **Least** **Mean** **Square** **algorithm**. This is used to normalize the high input power of input vector u (t). When a high power signal comes in input vector, then LMS filter suffers gradient noise amplification problems. To overcome this problem, adjustment in tap weight vector of the filter at iteration (n+1). Step size of the filter is under the control of the designer. It supports the real value’s error e (n) as well as complex conjugate error *e(n)[2],[6],[7]. The mathematical relation of the filter is given bellow.

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The LMS **algorithm** is a stochastic gradient **algorithm**; it iterates each tap weight of a transversal filter in the direction of the gradient of the squared magnitude of the error signal with respect the tap weight [2]. The main demerit of the LMS **algorithm** is that it is sensitive to the scaling of its input. The stability of the LMS **algorithm** is guaranteed by a learning rate µ, which is not easily chosen due to its sensitivity. This problem can be solved with the help of the Normalized **Least** **Mean** **Square** **Algorithm** (NLMS), which is a variant of the LMS **algorithm**, by normalizing with the power of the input. Further, slow convergence and high sensitivity to the Eigen value spread are some of the problems associated with the LMS **algorithm** which can be solved by using the RLS **algorithm**. The RLS **algorithm** represents increased complexity, computational cost and fidelity [4].

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This paper describes a system which is used to remove Wow and Flutter from audio signal using **Least** **Mean** **Square** **Algorithm**. It is impossible to completely remove Wow and Flutter from audio signal but its effect can be reduced significantly. It occurs during the process of sound reproduction. It is the group of tones created by the irregularities in turntables or tape drive speed during reproduction, duplication or recording. Wow occurs due to irregularities at low frequency whereas at high frequency irregularities, Flutter occurs. **Least** **Mean** **Square** **Algorithm** uses **Adaptive** Filter which adjusts their coefficient in order to minimize the required wobble effects in audio signal. Results show that LMS has comprehensively diminished the effects of wow and flutter.

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The normalized **least** **mean** **square** **algorithm** is an iterative **adaptive** **algorithm** that can be used in the highly time varying signal environment. The NLMS **algorithm** uses the estimates of the gradient vector from the available data. The NLMS **algorithm** incorporates an iterative procedure that makes successive corrections to the weights vector in the direction of the negative of the gradient vector which eventually leads to the minimum **mean** **square** error. The transfer function h n of the NLMS **adaptive** filter is given by

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Recently **Adaptive** filtering schemes have frequently used in communications, signal processing, control and many other applications. **Adaptive** filtering scheme become the most popular due to their simplicity and robustness. The elementary object of an **adaptive** filter is to adapt its parameters according to certain criterion to minimize a specific objective function like MSE, noise variance etc and maximize a specific objective function like SINR ratio, gain, likelihood, output power etc [2]. The **adaptive** **algorithm** adapting the filter parameters varies with the application object, among these **adaptive** filtering algorithms **Least** **Mean** **Square** **algorithm** and Recursive **Least** Squares **algorithm** have become the most popular **adaptive** filtering algorithms as a consequence of their simplicity and robustness [3, 4]. In recent decades, Widrow and Hoff's LMS **algorithm** [3] has been successfully used in various applications such as plant identification, channel equalization, array signal processing, etc [4]. The criterion of this **algorithm** is minimum **mean** **square** error between the desire response and the error signal. It has the advantages of robustness, good tracking capabilities, simplicity in terms of computational load and easiness of implementation. RLS **algorithm** can lead to the optimal estimate in the **mean**-**square** error sense. However, the assumption on which it based is that the error signal between the system and model filter outputs is Gaussian. The performance of these **adaptive** filters is effect by the noise caused due to background when they process for identification of an unknown FIR filter [1]. For these reasons, the performance of the RLS filters can be deteriorated significantly but RLS **algorithm** has faster convergence speed and better control performance [9], so the MSE in RLS is reduced with compare to LMS **algorithm**. As well as we focus on the QR- RLS **algorithm** that has better performance and results over LMS, NLMS & RLS algorithms.

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It is a Normalized **Least** **Mean** **Square** **algorithm**. This is used to normalize the high input power of input vector u (t). When a high power signal comes in input vector, then LMS filter suffers gradient noise amplification problems. To overcome this problem, adjustment in tap weight vector of the filter at iteration (n+1). Step size of the filter is under the control of the designer. It supports the real value’s error e (n) as well as complex conjugate error *e(n)[2],[6].

The (LMS) **least** **mean** **square** **algorithm** is the simple, most powerful and famous **adaptive** algorithms which can be applied easily in real-time. The LMS **algorithm** which was developed by Widrow, trains its input correlation matrix and minimizes the MSE. The ratio of maximum to minimum eigen values has an important influence on the speed of convergence. If this ratio is small, it would speed up the rate of convergence, and if it is large, it would reduce the speed rate of convergence. The LMS **algorithm** makes use of the steepest descent **algorithm** in which the weights are updated by using the following equation Where is the weight, is the true gradient vector defined by , k is the kth sampling instant, and is the step size. It should be noted that the stability and the convergence rate depends on the value of step size. It is clear that in order to be able to compute, needs information about and as shown in equation.

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We notice that during the weight update the error with n1 delays wereused. Then the filtering unit uses the weights delayed by n2 cycles. The modified DLMS **algorithm** decouples computations of the error-computation block and the weight-update block and allows us to perform optimal pipelining by feed forward cut-set retiming of both these sections separately to

These noise and interference makesthe incorrect diag- nosis of the ECG signal [1-3]. So, theremoval of these noise and interference from the ECG signalhas become very crucial. Different types of digital filters (FIRand IIR) have been used to solve the problem [3-5]. However,it is difficult to apply these filters with fixed coefficients toreduce different types of noises, because the ECG sig- nal isknown as a non-stationary signal. Recently, adap- tive filteringhas Become effective and popular methods for processing andanalysis of the ECG signal [6-8]. It is well known thatadaptive filters with **least** **mean** **square** (LMS) **algorithm** showgood performance for process- ing and analysis of signal whichare non-stationary [1]. And in this study, we have usedadaptive LMS and nor- malized **least** **mean** **square** (NLMS)filter to denoise the ECG signal. We also have evaluated theirperformance. But it is shown that NLMS filter removes allspecified noise (mentioned above) more significantly.

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The above-mentioned advantages motivate us to analyze the proposed sign regressor **least** **mean** fourth (SRLMF) **adaptive** **algorithm**. In this paper, the **mean**-**square** analysis, the convergence analysis, the tracking analysis, and the transient analysis of the SRLMF **algorithm** are carried out. The framework used in this work relies on energy conservation arguments [18]. Expressions are evaluated for the steady-state excess-**mean**-**square** error (EMSE) of the SRLMF **algorithm** in a stationary environment. A condition for the convergence of the **mean** behavior of the SRLMF **algorithm** is also derived. Also, expressions for the tracking EMSE in a nonstationary environment are presented. An optimum value of the step-size μ is also evaluated. Moreover, an extension of the weighted variance relation is provided in order to derive expressions for the **mean**-**square** error (MSE) and the **mean**-**square** deviation (MSD) of the proposed **algorithm** during the transient phase. From the simulation results it is shown that both the SRLMF **algorithm** and the **least** **mean** fourth (LMF) **algorithm** [19] have a similar performance for the same steady-state EMSE. Moreover, the results show that the theoretical and simulated results are in good agreement.

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ABSTRACT: **Adaptive** filter **algorithm** is a widely used method in communication systems, control systems, digital signal processing etc. This method helps to find out the unknown parameters iteratively by adjusting the filter parameters. There are many efficient **adaptive** filter algorithms. But among them, the basic algorithms are: **Least** **Mean** **Square** (LMS) and Recursive **Least** **Square** (RLS) Algorithms. The LMS **algorithm** is based on gradient optimization and the RLS **algorithm** is based on direct form FIR and lattice realization. The RLS **algorithm** is popular because of its fast convergence although the LMS **algorithm** is very simple to implement. There are modified LMS algorithms and they are: Leaky **Least** **Mean** **Square** (LLMS) **Algorithm** and Normalized **Least** **Mean** **Square** (NLMS) **Algorithm**. „Step size‟ is an important parameter which is used to implement any of these LMS algorithms. In case of RLS **algorithm**, one term „forgetting factor‟ plays an important role in times of implementing any system.

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high order harmonics of the current signal. However, the FFT estimation **algorithm** need to acquire the past current data firstly, and then analyze it. The computation task of using FFT to identify harmonics is burden and it inevitably gets delayed for about two periods. Furthermore, the real-time performance of this **algorithm** is not good. The precision of the estimated parameter may be reduced due to frequency spectrum leakage and picket-fence effects. Kalman Filter is also one of the most useful algorithms for harmonic identification, but its dynamic tracing performance will be seriously reduced when the tested signal is time-varying. Besides, **Least** **Mean** **Square**, as well as Recurisive **Least** Squares, is also used in harmonic identification. But they are not that effective when used to estimate harmonics online. During the real-time detection, since their estimation precision and real-time performance are unqualified, they are not extensively used.

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Abstract: The hardware implementation of **adaptive** filters is a challenging issue in real-time practical noise cancellation, echo cancellation, prediction and system identification applications. An **adaptive** filter is a kind of filter that changes and updates its specifications according to the application automatically and does not need user intervention to do the changes. A digital filter takes a digital input, gives a digital output, and consists of digital components. An **adaptive** filter consists of two blocks. The first block named Filter can be a FIR or IIR digital filter. Nowadays FIR filters are more common, because they are less complicated and more stable. The second block is Weight Adaptation that updates filter block weights according to adaptation **algorithm** to decrease error signal and achieve filter model. In our project we are considering **adaptive** **least** **mean** **square** (LMS) filter and self-correcting **adaptive** filter called as delayed **least** **mean** **square** (DLMS)**algorithm** architectures.

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NLMS **adaptive** **algorithm** to remove noise in voice communication systems. The Acoustic Noise Cancellation (ANC) is modeled in Simulink using digital filters, especially **adaptive** Normalized **Least** **Mean** **Square** (NLMS) **algorithm**. Finally the real- time characteristics of this module are verified on a Digital Signal Processor (DSP) TMS 320 C6713. The paper is structured as follows: section II presents digital **adaptive** filters for noise cancelling, section III presents the DSK TMS320C6713 card, section IV presents simulation results, Section V presents module design and Section VI concludes this paper.

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