1. Frequency Domain Adaptive Filtering Project Supervisor Dr. Edward Jones Myles Ó Fríl

2. Adaptive Filters  Digital Filter  Adaptive Algorithm  Convolution  Time Domain Algorithms  The LMS Algorithm

3. System Identification

4. Echo Cancellation

5. Frequency Domain Filtering  Discrete Fourier Transform  Fast Fourier Transform  N a power of two  Time Convolution Theorem  Efficiency  Overlap Save

6. Overlap Save Filtering

7. Frequency Domain Adaptive Filtering Algorithm  Fast LMS  Overlap Save Filtering  Block Diagram of Fast LMS

9. Memory Comparison  LMS N inputs + N filter coefficients = 2N  Fast LMS 15 N in total

10. Computational Comparison  LMS 2N x N  Fast LMS 15N log2 (2N) + 10Nfor 5 FFTs + 28Nfor rest of algorithm  Cross Over Point N a power of two 128

11. LMS V Fast LMS

12. Implementation  The NIDAQ Card  Threads

13. Further Applications  Training Period  Decision Maker  Time Domain  Frequency Domain  Adaptive Equalizer

14. Summary  Adaptive Filters  System Identification  Frequency Domain Filtering  Frequency Domain Adaptive Algorithm  Memory/Computational Comparison  Implementation Any Questions?