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UNIT IV

ADAPTIVE FILTERS

1. What is an Adaptive Filter?An adaptive filter is essentially a digital filter with self adjusting

characteristics. It adapts automatically to changes in its input signal.

2. What is the difference between the conventional filter and the adaptivefilter?

In the conventional filter, the filter coefficients(weights) remain fixed while

the filters weights are variable in the adaptive filter.

3. What are the two distinct parts in an adaptive filter?(i) Digital Filter [with adjustable filter coefficients](ii) Adaptive Algorithm [to adjust the filter coefficients]

4. List some important applications of adaptive filter.(i) Noise cancellation(ii)

Echo cancellation(iii) Channel Equalization

(iv) Removal of Ocular Artefacts from Human EEG(v) Line Enhancer(vi) Linear Combiner(vii) System Modeller(viii) Self Tuning Filter

5. What are the various adaptive algorithms employed in adaptive filters?(i) Weiner Filter Algorithm(ii) Least Mean Square(LMS) Algorithm(iii) Recursive Least Squares(RLS) Algorithm(iv) Kalman Filtering Algorithm

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6. When adaptive filters are used?Adaptive filters are used

(i) When it is necessary for the filter coefficients to be varied.(ii) If there is any spectral overlap between the noise and the signal.(iii) If the band occupied by the noise is unknown and varies with time.

7. Give the formula to compute the output of an adaptive filter?nk = ()

8. Write the Weiner Hopf Equation.Wopt = R- 1 Pwhere R is the Autocorrelation Matrix and P is the Cross Correlation

Vector

9. What is Wiener Filter?The optimum linear filter in the sense of minimizing the Mean Square

Error(MSE) is called Wiener Filter.

10.Under what condition , the filter weight has the optimal value?The filter weight is having its optimal value only at the bottom point of the

error performance surface where the Gradient is zero.

11.What are the limitations of Wiener Filter?(i) It requires matrix inversion which is time consuming(ii) It involves Auto Correlation matrix R and the Cross Correlation

vector P both of which are not known a priori.

(iii) If the signals are not stationary, the R and P will vary w.r.t time and soWopt have to be computed separately.

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12.Write the steepest descent algorithm(LMS)WK+1 = WK- K

W is the weight vector, is the true Gradient Vector and is a factor

controls the stability and the rate of convergence

13.Write the Widrow Hopf equationWK+1(i) = WK(i) +2 ekx k-i

14.What are the practical limitations that are encountered in LMS Algorithm?(i) Effects of non stationarity(ii) Effects of signal components on input interference channel(iii) Coefficient drift.(iv) Computer wordlength requirements

15.What do you mean by Coefficient Drift?In the presence of certain type of narrow band input signals, the filter

coefficient may drift slightly from its optimal value and grow slowly,

eventually exceeds the permissible wordlength due to long term degradation

in its performance. This drift is known as Coefficient Drift. This can be

overcome by introducing a leakage factor.

16.What are limitations in RLS algorithm?(i) Signal Blowup(ii) Computer Round off Errors

17.Name the two factorization algorithms to overcome limitations in RLSalgorithm?

(i) Square Root Algorithm(ii) UD Algorithm

18.What is meant by Electro Ocular Gram(EOG)?Blinking of eyes or moving the eyes produces larger electrical potentials

around the eye. This is known as Electro Ocular Gram.

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19.What do you mean by Ocular Artefact[OA]?The EOG signal spreads across the scalp which gets contaminated with the

EEG signal leads to Ocular Artefact. Ocular Artefact leads to difficulty in

distinguishing between the normal and the abnormal brains.

Egs: Brain Damaged Babies and Frontal Tumors.

20.How does Echo arise?Echo arises due to any mismatch in impedance.

21.What is Channel Equalization?The method of inserting equalizer over a telephone channel at the receiver

side in order to compensate attenuation distortion or phase distortion or any

amplitude distortion occuring in it. Inter Symbol Interference can also beeliminated.

22.Draw the block diagram of an adaptive filter as a noise canceller.

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23.Draw the block diagram of an adaptive filter as a Line Enhancer

24.Draw the block diagram of an adaptive filter as a Self Tuning Filter.

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25.Draw the block diagram of an adaptive filter as a System Modeller.

26. Draw the block diagram of an adaptive filter as a Linear Combiner.

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27.What is the significance of LMS algorithm?The filter weights are updated from sample to sample. The LMS algorithm is

a practical method of obtaining weight estimates in real time and without the

help of any matrix inversion.

28.Give the steps to update the next filter weight in LMS AlgorithmStep1: Initially , set each weight wk(i) , I = 0 ,1,2,..,N-1 to any arbitrary

fixed value such as 0. For each subsequent sampling instant

of k, where k=1,2,3, etc, compute the following steps.

Step 2: Compute the filter output.

Step 3: Compute the error estimate

Step 4: Update the next filter weight.