1. Adaptive Filter Design & Implementation
Digital Signal Processing Project
Dr. Pawan K. Ajmera
EEE F434
Adaptive Filter Design & Implementation
Rishabh Bhardwaj 2014A3PS179P
Aditya Manglik 2014A3PS296P

2. Linear Filters Linear filters :
filter output is a linear function of the filter input .
Design methods:
The classical approach:-
frequency-selective filters such as
high pass/ low pass / band pass / notch filters etc.

3. What is a Digital Filter?
A Digital Filter is a system that performs mathematical operations on a sampled discrete-time signal to reduce or enhance certain aspects of that signal.

4. Limitations of fixed coefficient digital filter
Time varying noise frequency cannot be filtered easily, as is usually the case in practical signals
Overlapping bands of signals and noise, which is a critical problem in real time systems

5. Optimal filter design
Coefficients are updated at every iteration according to the error function
Mostly based on minimizing the mean-square value
of the error signal

6. Adaptive filter
Signal and/or noise characteristics are often nonstationary and the statistical parameters vary with time
Adaptive filter has an adaptation algorithm, that is meant to monitor the environment and vary the filter transfer function accordingly
Based on the actual signals received, the algorithm attempts to find the optimum filter design

7. Weiner Filter
In a stationary environment, the filter is expected to converge, to the Wiener filter
In a nonstationary environment, the filter is expected to track time variations and vary its filter coefficients accordingly!

8. Adaptive filter The basic operation now involves two processes :
1. Filtering process, which produces an output signal in response to a given input signal.
2. Adaptation process, which aims to adjust the filter parameters (filter transfer function) to the (possibly time- varying) environment. Often, the (average) square value of the error signal is used as the optimization criterion
Adaptive filter

9. Why not IIR?
The generalization to adaptive IIR filters leads to stability problems
It’s common to use
a FIR digital filter with
adjustable
coefficients.

10. Adaptive Filter Filtering Principle

11. Least Mean Squares(LMS) Algorithm
Most popular adaptation algorithm is LMS.
Defines cost function as mean-squared error.
Based on the method of steepest descent
“Move towards the minimum on the error surface to get to minimum gradient of the error surface estimated at every iteration!”

12. LMS implementation
Widrow-Hoff LMS Algorithm

13. LMS Algorithm

14. RLS implementation

15. NLMS (Normalized Least Mean Squares) Algorithm
The main drawback of the simple LMS algorithm is that it is sensitive to the scaling of its input. This makes it very hard to choose a learning rate µ that guarantees stability of the algorithm. The Normalized least mean squares (NLMS) filter is a variant of the LMS algorithm. The benefit is that it solves this problem by normalizing with the power of the input.

16. Performance Comparisons between different algorithms

17. Applications of Adaptive Digital Signal Processing

18. Four Typical Applications of Adaptive Filters

20. Acoustic Echo Cancellation

21. New Trends in Adaptive Filtering
Partial Updating Weights.
Sub-band adaptive filtering.
Adaptive Kalman filtering.
Affine Projection Method.
Time-Space adaptive processing.
Non-Linear adaptive filtering:-
Neural Networks.
The Volterra Series Algorithm .
Genetic & Fuzzy.
Blind Adaptive Filtering.

22. Thank You