International Journal of Advanced Engineering, Management and Science (IJAEMS)
[Vol-1, Issue-2, May- 2015] ISSN: 2454-1311
Comparative study of Adaptive Filter Aakash kadian, Hemant dalal Abstract— Main goal of this paper is to study the different types of adaptive filters and their uses. An adaptive filter is a digital filter, which self adjust their impulse response according to the original signal so that it can track out the original signal or noise free signal from the nosey signal. In this paper different types of adaptive filters LMS (Least mean square), NLMS (Normalized Least mean square), RLS (Recursive Least square) and the uses of these in ANC (Adaptive noise cancellation) application of adaptive filter are study. Keywords— Adaptive filter, LMS, NLMS, RLS, ANC I.
INTRODUCTION
An adaptive filter is a digital filter with self adjusting characteristics and tracking capacities. Adaptive filter have the ability to adjust their impulse response to filter out the correlated signal. Adaptive filter don’t required or little required of the signal knowledge and the noise characteristics that is correlated to the original signal which required to be estimated. Adaptive filters are not like the non-adaptive or fixed filters which have static or fixed filter coefficients. Adaptive filters are designed to change their coefficients according to a desired or required original signal. This distinguish feature of adaptive filters is use to improve the performance during operation without any intervention from the user. [1] [3] An adaptive filter divided into two parts: one is a digital filter with adjustable coefficients and another is an adaptive algorithm which is used to adjust or modify the coefficients of the filter. The important properties of adaptive filter are that it can work effective in unknown environment, and to track the input signal of time-varying characteristics. Adaptive filter has been used in communications, control and many other systems. II.
ADAPTIVE FILTER TYPES
An adaptive process provides a mechanism for the adaptive control and having the adjustable set of parameters which used in the filtering process. These two processes work interactively with each other. [1]
The filtering process has a profound effect on the operation of the algorithm as a whole. The impulse response of a linear filter determines the filter’s memory. On this basis, we may classify filters into two forms, 1. Finite duration impulse response (FIR) 2. Infinite duration impulse response (IIR) filters, which has been characterized by finite memory and infinitely long memory respectively. Although both IIR and FIR filters have been considered for adaptive filtering, but the FIR filter is used far for the most practical and widely used. The reason for this is the only adjustable zeros. Due to this, FIR filter is free from the stability problems associated as with the adaptive IIR filter, which have adjustable poles as well as zeros. However, the stability of FIR filter depends critically on the algorithm for adjusting its coefficients. 1. ANC(Adaptive Noise Cancellation) Adaptive noise cancellation is a technique in which noise is reduced by using adaptive filter. Adaptive filters are used where the signal is non stationary or having time varying signal environment. [1] Adaptive filter adjust their coefficients to minimize an error application of adaptive filters includes adaptive noise cancellation, which is used to remove noise or interference from noisy speech signal. In ANC, the corrupted signal is passed through a filter that tends to suppress the noise while leaving the original signal unchanged. [11] Figure 1.1 shows the adaptive noise cancellation Primary Sensor
Sk + HNk
Output
Signal Source
∑
Sk ĤNk
H Noise Source
Adaptive
Nk
Reference Sensor
Filter Ĥ
Fig. 1.1 Adaptive Noise Canceller Page | 68
International Journal of Advanced Engineering, Management and Science (IJAEMS)
In this setup, the signal path from the noise source is passed to the primary sensor as an unknown FIR channel H. The adaptive filter to the noise recorded at the reference sensor, and then an adaptive algorithm is used to train the adaptive filter to match or estimate the characteristics of the unknown channel H. If the estimated characteristics of the unknown channel have negligible differences as compared to the actual characteristics, the noise components in the corrupted signal can be cancelled to obtain the desired signal. 2. LMS (Least Mean Square) Least mean square (LMS) algorithm is an adaptive algorithm, which was invented by Widrow and Hoff in 1960. The LMS algorithm is extremely simple since it minimizes the instantaneous square error instead of the mean square error, using a simple gradient-based optimization method. This algorithm achieves the Wiener solution in mean sense. The Least Mean Square adaptive algorithm is the most widely used real time filtering algorithm due to its computing requirements. The adaptive LMS algorithm is chosen because of its simplicity, hardware efficiency and stability. [12][8] From the steepest descent algorithm
∂J ( w ) = −2 p + 2 Rw ∂w
wˆ ( n + 1) = wˆ ( n) + µ .e ( n)
The parameter µ is termed the adaptation gain (learning rate, step size) and controls the speed of convergence
w[ n + 1] = w[ n ] + µ e[ n ] x[ n ]
w[n + 1] = w[n] + µ ( x[n](d[n] − x[n] H w[n])) 3. NLMS(Normalised Least Mean Square) The normalized LMS (NLMS) algorithm is a modified form of the standard LMS algorithm. [8] The NLMS algorithm updates the coefficients of an adaptive filter by using the following equation:
uˆ ( n )
2
wˆ ( n + 1) = wˆ ( n ) + µ ( n ).e ( n ).uˆ ( n ) Here
µ ˆ( n ) =
µ uˆ ( n)
2
In the previous equation, the NLMS algorithm becomes the same as the standard LMS algorithm except that the NLMS algorithm has a time-varying step size μ(n). This step size can improve the convergence speed of the adaptive filter. 4. RLS(Recursive Least Squares) 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. In the derivation of the RLS, the input signals are considered deterministic, while for the LMS and similar algorithm they are considered stochastic. Compared to most of its competitors, the RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity.[14] III.
w[n + 1] = w[n] + µ ( −∇J | w[n ] ) w[ n + 1] = w[ n ] + µ ( p − Rw[ n ])
u (n)
You also can rewrite the above equation to the following equation:
And
So that the “weights update equation”
[Vol-1, Issue-2, May- 2015] ISSN: 2454-1311
CONCLUSION
This paper presents the adaptive filter and use of the adaptive filter as adaptive noise cancellation. ANC used to reduce the noise signal from the original signal by using adaptive filter. Adaptive filter has capability to adapt the coefficients of the filter according to the desired signal. For this different algorithms are used, these are Least mean square (LMS), modified LMS i.e. Normalised least mean square (NLMS) and RLS (Recursive least square). REFERENCES [1] [2]
[3]
John G Proakis “Digital Signal Processing” 3rd edition, Perntice Hall of India. B. Widrow, Adaptive filters 1: Fundamentals, Stanford Electronics Lab., Stanford Univ., Rep. SUSEL-66-126, Dec. 1966. Simon Haykin, “Adaptive Filter Theory”, Prentice Hall, 4th edition. Page | 68
International Journal of Advanced Engineering, Management and Science (IJAEMS)
[Vol-1, Issue-2, May- 2015] ISSN: 2454-1311
[4]
G.Amjad Khan, Dr. K.E. SreenivasaMurthy, J. Satyanarayana “Noise cancellation in Speech Signals by Using a Constrained Stability LMS Algorithm” International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 1, Jan-Feb 2012, pp. 426-430. [5] Jafar Ramadhan Mohammed1, Muhammad Safder Shafi2, Sahar Imtiaz2, Rafay Iqbal Ansari2, and Mansoor Khan2 “An Efficient Adaptive Noise Cancellation Scheme Using ALE and NLMS Filters” International Journal of Electrical and Computer Engineering (IJECE) Vol.2, No.3, June 2012, pp. 325~332 ISSN: 2088-8708 _325. [6] Pranjali M. Awachat, S.S. Godbole “A Design Approach For Noise Cancellation In Adaptive LMS Predictor Using MATLAB” International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, Julyaugust 2012, pp.2388-2391 2388. [7] Mamta M. Mahajan e al. “Design of Least Mean Square Algorithm for Adaptive Noise Canceller” International Journal of Advanced Engineering Sciences And Technology Vol No. 5, Issue No. 2,2012 172 –176. [8] Jashvir Chhikara and Jagbir Singh “Noise Cancellation Using Adaptive Algorithms” International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.3, pp-792-795 ISSN: 2249-6645, May-June 2012. [9] Cristina Gabriela Saracin, Marin Saracin, Mihai Dascalu, Ana-Maria Lepar “Echo Cancellation Using The LMS Algorithm” U.P.B. Sci. Bull., Series C, Vol. 71, Iss. 4, 2009 ISSN 1454-234x. [10] Jashvir Chhikara and Jagbir Singh “Noise Cancellation Using Adaptive Algorithms " International Journal of Modern Engineering Research (IJMER) Volume 50, Nov 4,2009. [11] Raj Kumar Thenua and S.K. Agarwal “Simulation And Performance Analysis Of Adaptive Filter In Noise Cancellation” International Journal of Engineering Science and Technology Vol. 2(9), 2010, 4373-437. [12] Sayed. A. Hadei and M. lotfizad ”A Family Of Adaptive Filter Algorithms In Noise Cancellation For Speech Enhancement” International Journal of Computer and Electrical Engineering, Vol. 2, No. 2, 1793-8163,April 2010.
Page | 69