1. Noise Cancellation
LMS Adaptive Filter
Ashish Kumar Meshram
Roll No. mt1402102002
M.Tech. Communication & Signal Processing
Department of Electrical Engineering
IIT – Indore | EE641 | Advance Signal Processing

2. IIT – Indore | EE641 | Advance Signal Processing 1
Content
Introduction
Noise Cancellation
Adaptive Signal Processing
Least Mean Square Algorithm
Implementation
Results
Conclusion

3. IIT – Indore | EE641 | Advance Signal Processing 2
Adaptive Noise Cancellation
Primary Source
Reference Input
𝑥(𝑛)
𝑑 𝑛 = 𝑥 𝑛 + 𝑠(𝑛) 𝑒 𝑛 = 𝑑 𝑛 − 𝑦(𝑛)
𝑦(𝑛)
𝑢(𝑛)
Adaptive Filter
+
-
+
+
𝑠(𝑛)
Noise Source

4. IIT – Indore | EE641 | Advance Signal Processing 3
Algorithm: Least Mean Square (LMS)
Filter output:
Estimation error or error signal:
Tap-weight adaptation:
𝒖 𝑛 = [𝑢 𝑛 𝑢 𝑛 − 1 … … 𝑢 𝑛 − 𝑀 + 1 ] 𝑇
𝒘 𝑛 = [𝑤1 𝑤2 … … . . 𝑤 𝑀−1] 𝑇
Reference Signal:
Tap weight vector:
𝜇Step size:
Input Parameters
𝑀Filter Order:
Initialization
𝒘 𝑛 = [0 0 0 … … 0] 𝑇Tap weight vector:
𝑦 𝑛 = 𝒘 𝐻
𝑛 𝒖(𝑛)
𝑒 𝑛 = 𝑑 𝑛 − 𝑦(𝑛)
𝒘 n + 1 = 𝒘 𝑛 + 𝜇𝒖(𝑛)𝑒∗
(𝑛)
For 𝑛 = 1,2,3 … . . compute

5. IIT – Indore | EE641 | Advance Signal Processing 4
MATLAB Implementation
function [v1 v2] = corrnoise(g,a,b)Correlated Noise Generator
function [e] = anc(x,mu,M,w)Adaptive Noise Cancellation Using LMS
function [W,e] = aflms(d,u,mu,M,w)LMS Adaptive Filter
𝑣1 𝑛 = 𝑎1 𝑣1 𝑛 − 1 + 𝑏1 𝑔(𝑛)
𝑣2 𝑛 = 𝑎2 𝑣2 𝑛 − 1 + 𝑏2 𝑔(𝑛)
𝑔 𝑛 = 𝑁(0,1)
x
Mu
M
w
Signal to be processed
Step Size
Number of tap weight
Initial tap weight
INPUT:
e Noise Cancelled Signal
OUTPUT:
d
u
Mu
M
w
Signal to be processed
Reference Signal
Step Size
Number of tap weight
Initial tap weight
INPUT:
e
W
Noise Cancelled Signal
Weight Matrix
OUTPUT:

6. IIT – Indore | EE641 | Advance Signal Processing 5
Results
M = 32, mu = 0.05 M = 32, mu = 0.005
[E] = anc(sin(linspace(0,4*pi,100)),0.05,32,[]); [E] = anc(sin(linspace(0,4*pi,100)),0.005,32,[]);

7. IIT – Indore | EE641 | Advance Signal Processing 6
References
 Simon Haykin, Adaptive Filter Theory, 3e
 Monson H Hayes, Statistical Digital Signal Processing and Modeling
 Ali H. Sayed, Adaptive Filters

8. THANK YOU