1. EE 426 DIGITAL SIGNAL PROCESSING TERM PROJECT Objective: Adaptive Noise Cancellation

2. Introduction An adaptive filter is essentially a digital filter with self- adjusting characteristics. Adaptive filters are central topic in the sub-area of Digital Signal Processing. Widely used algorithms in adaptive signal processing: - The Widrow-Hoff or Least Mean Squares ( LMS ) - Recursive Least Squares ( RLS ) Also Neural Network Approach is used for Noise Cancellation.

3. An illustration of spectral overlap between a signal and strong interference w magnitude Interference spectrum Desired signal spectrum

4. Block diagram of an adaptive filter as a noise canceller Digital filter Adaptive algorithm  yk = sk + nk (signal + noise) xk noisenk’ noise estimate ek = sk (signal estimate) + -

5. Adaptive filters as a noise canceller The signal, xk, is a measure of the contaminated signal which is correlated in some way with n k. x k is processed by the digital filter to produce an estimate, n k ’, of n k. An estimate of the desired signal is then obtained by subtracting the digital filter output, n k ’, from the contaminated signal, y k : s k ’ = y k - n k ’ = s k + n k - n k ’

6. Finite Impulse Response filter structure z^-1  xkxk x k-1 x k-2 x k-(N-1) w k(0) w k(1) w k(2) w k(n-1) N-1 n k’ =  w k(i) x k-i i=0

7. Normalised Least Mean Square Algorithm

8. The main Matlab program that we used to compute Normalised LMS % the LMS algorithm needs two FOR-LOOP for i = ord+1:length(x), for j=1:ord+1, R(j)=[r1(i-(j-1))]; R2(j)=[r1(i-(j-1))^2]; end n1(i)=sum(R2); y(i)=sum(W(:,i).*R); % sum the outputs of the tapped delay lines, %this gives us the filter output e(i)=x(i)-y(i); % this is the output of the ANC W(:,i+1)=W(:,i)+mu*e(i)*R./n1(i); % find the TAPs for the next cycle end

9. An illustration of the variations in the filter weights wkwk w opt k

10. LMS Based FIR adaptive filter is characterized by the following equations: For the digital filter, N-1 n k’ =  w k(i) x k-i i=0 For the adaptive algorithm, W k+1 = W k + 2  e k X k where e k= y k - W k’ X k

11. Application example 1 Adaptive telephone echo cancellation HybridAF Hybrid Channel + + ykyk y k’ ekek xkxk N-1 y k =  w k(i) x k-i+ s k i=0 N-1 y k ’ =  w k(i) x k-j i=0

12. Adaptive telephone echo cancellation Xk = incoming signal (far-end speaker) Yk = estimation of echo subtracting from the return signal Sk = near-end speaker + additive noise Wk = impulse response of echo system Yk’ = echo subtractor from the normal return signal

13. Application example 2 Loudspeaking telephones AF + + Hybrid loudspeaker microphone

14. Conclusion We noticed that in both case we applied for noise cancellation, we achived to cancel the noise effectively on desired signal. This study can be a good background for our future studies.

15. Future Work We can apply same method by using the idea of Neural Network Approach. Investigation on realization of electronic systems for Real-time applications.

16. End of Presentation