Overview of Noise Reduction Techniques in Digital Signal Processing

1. 2004 COMP.DSP CONFERENCE Survey of Noise Reduction Techniques Maurice Givens

2. NOISE REDUCTION TECHNIQUES • Minimum Mean-Squared Error (MMSE) • Least Squares (LS) • Recursive Least Squares (RLS) • Least Mean Squares (LMS, NLMS) • Coefficient Shrinkage • Fast Fourier Transform (FFT) Decomposition • Wavelet Transform Decomposition (CWT, DWT) • Spectral (Sub-Band) Subtraction • Blind Adaptive Filter (BAF) • Sub-Band Decomposition Using Orthogonal Filter Banks • Wavelet Decomposition • Fast Fourier Transform (FFT) Decomposition • Frequency Sampling Filter (FSF) decomposition

3. MINIMUM MEAN-SQUARED ERROR • LS, RLS, LMS Similar Operation • Seek to minimize mean-squared error • Will Look At LMS

4. LMS • Two Types Of Noise Reduction Techniques With LMS • Adaptive Noise Cancellation (ANC) • Adaptive Line Enhancement (ALE) • Similar Configurations • h(n+1) = h(n) + m e(n) x(n) • x(n)T x(n)

5. ANC CONFIGURATION + S Reference Noise - Input With Noise Adaptive Filter

6. ANC CONFIGURATION • ANC Uses Adaptive Filter For MMSE • ANC Requires Reference Noise Signal • ANC Based On Bernard Widrow’s LMS Adaptive Filter • ANC Can Only Recover Correlated Signals From Uncorrelated Noise • Error Signal Is Recovered (Denoised) Signal

7. ANC IMPLEMENTATION Reference Noise Seismometer Signal Seismometers

8. ALE CONFIGURATION + Reference Noise S - t Adaptive Filter

9. ALE CONFIGURATION • ALE Uses Adaptive Filter For MMSE • ALE Does Not Require Reference Noise Signal • ALE Uses Delay To Produce Reference Signal • ALE Can Only Recover Correlated Signals From Uncorrelated Noise • ALE Based On Bernard Widrow’s LMS Adaptive Filter • Filter Output Signal Is Recovered (Denoised) Signal

10. ALE CONFIGURATION • Sample of Noisy Signal

11. ALE CONFIGURATION • Recovered Signal Using ALE

12. ALE IMPLEMENTATION • Example of Noise and Tone on a Speech Segment Speech With Tone Cleaned Speech Speech With Noise Cleaned Speech

13. COEFFICIENT SHRINKAGE • Fast Fourier Transform • Decomposition Of Signal Using Orthogonal Sine - Cosine Basis Set • White Noise Shows As Constant “Level” In Decomposition • Values Of Fourier Transform Below A Threshold Are Reduced to Zero Or Reduced By Some Value • Inverse Fourier Transform is Used To Produce Recovered Signal • Wavelet Transform • Decomposition Of Signal Using A Special Orthogonal Basis Set • White Noise Shows As Small Values, Not Necessarily Constant • Wavelet Transform Values Below A Threshold Are Reduced to Zero Or Reduced By Some Value • Inverse Wavelet Transform is Used To Produce Recovered Signal • Have Both Continuous (CWT) And Discrete (DWT) Wavelets

14. FAST FOURIER TRANSFORM • Noisy Signal

15. FAST FOURIER TRANSFORM • Fast Fourier Transform Of Noisy Signal

16. FAST FOURIER TRANSFORM • Fast Fourier Transform After Coefficient Shrinkage

17. FAST FOURIER TRANSFORM • Recovered Signal Using Coefficient Shrinkage

18. WAVELET DECOMPOSITION • Special Orthogonal High Pass And Low Pass Filters • Down Sample By 2 • Up Sample By 2

19. WAVELET TRANSFORM • Important Characteristics Of Wavelet Transform • Basis Function Need Not Be Orthogonal If Perfect Reconstruction Is Not Needed • Wavelet Transform Very Good For Maintaining Edges In Signal • Wavelet Transform Excellent For Image Noise Reduction Because Images Have Sharp Edges • Wavelet Transform Not Very Good For Signals Like Speech When Noise Is High In Level • DWT Not Discrete Version Of CWT Like Fourier Transform And Discrete Fourier Transform

20. COEFFICIENT SHRINKAGE • Variant Can Use Both FFT and DWT • Astro-Physics Professor At U of C Needed Noise Reduction For Cosmic Pulses Recorded. • Pulses In Middle Of Radio Spectrum • Could Not Recover With FFT Decomposition And Coefficient Shrinkage • Asked For Help

21. COEFFICIENT SHRINKAGE • Original Recorded Signal

22. COEFFICIENT SHRINKAGE • Recovered Signal With FFT Decomposition Alone

23. COEFFICIENT SHRINKAGE • Pulse Is Good Signal For DWT Decomposition

24. SPECTRAL SUBTRACTION • Fast Fourier Decomposition • Sub-Band Decomposition Using Filter Banks • Wavelet Decomposition (Sub-Band Decomposition Using Orthogonal Filter Banks) • Blind Adaptive Filter (BAF) • Frequency Sampling Filter Decomposition

25. GENERAL SCHEME • Spectral Subtraction Uses Same General Scheme • Decompose Signal Into Spectrum • Determine Signal-To-Noise Ratio For Each Decomposition Bin • Vary Level Of Each Decomposition Bin Based On SNR • Convert Decomposed Signal Back Into Recovered Signal (Inverse Decomposition)

26. SIGNAL DECOMPOSITION METHODS • FFT • Decomposes Signal Into Frequency Bins • SNR Of Each Bin Is Determined • Inverse FFT To Recover Denoised Signal • Filter Bank (QMF) • Bandpass Filters Decompose Signal Into Frequency Bands • SNR Of Each Band Is Determined • Inverse Filter And Superposition To Recover Denoised Signal S

27. SIGNAL DECOMPOSITION • Alternate Filter Bank Method S

28. SIGNAL DECOMPOSITION METHODS • Wavelet • Similar To Filter Bank • Can Be Low Pass And High Pass Filters Only • Can Be Bandpass Filters Called Modulated Cosine Filters • SNR Of Each Band Is Determined • Inverse Filter And Superposition To Recover Denoised Signal • Can Be Complete Wavelet Packet Tree

29. BLIND ADAPTIVE FLTER • BAF • Two Methods • First Is Not Spectral Subtraction By Itself • BAF Is Used To Determine Parameters Of Noise • Spectrum Derived From Parameters • FFT, QMF, Wavelet, Or FSF Decomposition • Noise Spectrum Used As Basis For Level Gain • Second Used By Itself • BAF Is Used To Determine Parameters Of Noise • Filter Signal With Inverse Parameters To Whiten Noise • Use Any Method To Reduce White Noise • Use Parameters To Recover Denoised Signal

30. NOISE CANCELLATION USING FSF • Similar To Filter Bank And FFT • Uses FSF For Decomposition • Calculates SNR For Each Frequency Band • Adjusts Level Of Each Frequency Band Based On SNR • Recovers Denoised Signal Through Superposition

31. Noise Cancellation • Block Diagram TO OTHER BANDS SIGNAL POWER COMPUTE GAIN FROM OTHER BANDS NOISE POWER Gk(n) X(n) S Y(n) FSF VAD FROM OTHER BANDS TO OTHER BANDS

32. FREQUENCY SAMPLING FILTER • FSF Comprises Two Basis Blocks • Comb Filter • Resonator FSF Comb Filter Resonator C(z) Rk(z)

33. COMB FILTER • Block Diagram S x(n) Z-N rN u(n) - • Comb Filter Not Necessary For Implementation

34. Resonator

35. RESONATOR • Block Diagram u(n) Z-1 - r cos(qk) S S y(n) - r2 Z-1 2 Z-1

36. GOOGLE RESONATOR SEARCH

37. VOICE ACTIVITY DETECTOR • Calculate Power In A Formant (Usually First)

38. DECISION LOGIC • Speech Present Based On Inequality • Gain Based On Inequality

39. GAIN MODIFICATION • Gain Factor Requires Post-Emphasis

40. OTHER CONSIDERATIONS • Output Level Is Lower After Noise Reduction • Solution: Increase Signal By Scaling • Add A Portion Of Original Signal To Noise-Reduced Output • Can Help Mitigate Tinny Sound • Helpful If Lower Level Signals Are Overly Suppressed • Perform Algorithm Fewer Times When Speech Is Absent • Perform Algorithm On Sub-Set Of Frequency Bins Each Sampling Period • Can Add Non-Linear Center Clipper To Algorithm

41. EXAMPLE • Recording From Live Cellular Traffic • Original Noisy Sample • After Noise Reduction • Original Noisy Sample • After Noise Reduction

42. QUESTIONS?