This document discusses adaptive noise cancellation using the least mean squares (LMS) algorithm. It begins by introducing limitations of fixed filters for time-varying noise frequencies and overlapping signal and noise bands. It then defines digital filters, noise cancellation, adaptive filters, and adaptive noise cancellation. The LMS algorithm is described as consisting of a filtering process and adaptive process to minimize the mean square of the error signal. Code is presented to implement the initial part, main body, and display results of an adaptive noise cancellation system using LMS. Applications are identified in echo and noise cancellation, acoustic echo cancellation, system identification, and noise removal from ECG signals.

1. ADAPTIVE NOISE
CANCELLATION

2. Group No. 01
Name: Robin Ray
Student ID: 1406066
Name: Mahmud Mohaimin
Student ID: 1406067
Name: Rafat Jamal Tazim
Student ID: 1406068
Name: Md. Mohiuddin Sumon
Student ID: 1406069

3. Motivation
Limitations of Fixed Filters
Time-varying Noise Frequency
Overlapping Bands of Signal & Noise

4. Digital Filter
A system that performs mathematical operations on
a sampled, discrete-time signal to reduce or enhance
certain aspects of that signal

5. Noise Cancellation
Method for reducing unwanted sound by
addition of a second sound specifically
designed to cancel the first

6. Adaptive Filter
A system with a linear filter that has a transfer function
controlled by variable parameters and a means to
adjust those parameters according to an optimization
algorithm

7. Adaptive Noise Cancellation
Input x(n), a noise source N1(n), is compared with a desired
signal d(n), which consists of a signal s(n) corrupted by another
noise N0(n). The adaptive filter coefficients adapt to cause the
error signal to be a noiseless version of the signal s(n)

8. LMS Algorithm
 An adaptive filtering algorithm used to mimic a desired filter
by finding the filter coefficients that relate to producing the
least mean square of the error signal
 Consists of 2 basic processes,
1. Filtering Process
2. Adaptive Process

9. LMS: Gradient Approximation Method
 2 Input Signals,
 yk = sk + nk
Where sk is desired signal
& nk is noise
 xk, is a measure of contaminating signal which
is someway correlated with nk
 xk gives estimate of nk, consider it 𝑛 𝑘
 Estimating sk, by subtracting the noise estimate,
𝑠 𝑘 = 𝑦 𝑘 − 𝑛 𝑘

10. LMS: Algorithm
𝑥 𝑘 =
𝑥 𝑘
𝑥 𝑘−1
⋮
⋮
𝑥 𝑘−(𝑁−1)
, vector correlated with
noise
𝑤 =
𝑤0
𝑤1
⋮
⋮
𝑤 𝑁−1
, set of adjustable weights with
N coefficients
• Approximations to
minimum mean
square error gives,
𝑠 𝑘 = 𝑒 𝑘 = 𝑦 𝑘 − 𝑛 𝑘
= 𝑦 𝑘 − 𝑤 𝑇 𝑥 𝑘
• Using methods of
steepest descent
method we get,
𝑤 𝑛+1 = 𝑤 𝑛 + 𝜇𝑒 𝑘 𝑥 𝑘

11. Code: Initial Part

12. Code: Main Body

13. Code: Displaying Results

14. Results

15. Results

16. Results

17. Advantages over Other Algorithms
Simplicity
Doesn’t require pertinent correlation function
Doesn’t require matrix inversion
Efficiency

18. Applications of Adaptive Noise
Cancellation
Echo & Noise Cancellation for Long Distance
Transmission

19. Applications of Adaptive Noise
Cancellation
Acoustic Echo Cancellation

20. Applications of Adaptive Noise
Cancellation
System Identification

21. Applications of Adaptive
Noise Cancellation
Noise Removal from ECG Signal

22. Limitations of this Project
Works only on real valued signals, not on complex
valued signals
Noise is taken as reference

23. Reference
 “Adaptive Filtering: Fundamentals of Least Mean Squares with
MATLAB” by Alexander D. Poularikas
 “Adaptive Filter Theory” by Symon Haykin
 DSP System Toolbox
(https://www.mathworks.com/help/dsp/adaptive-filters.html)

24. Thank You