2004 COMP.DSP CONFERENCE

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2004 COMP.DSP CONFERENCE

• Survey of Noise Reduction Techniques

Maurice Givens
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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

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MINIMUM MEAN-SQUARED ERROR

• LS, RLS, LMS Similar Operation
• Seek to minimize mean-squared error
• Will Look At LMS

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LMS

• Two Types Of Noise Reduction Techniques With LMS
• Adaptive Noise Cancellation (ANC)
• Adaptive Line Enhancement (ALE)
• Similar Configurations
• h(n1) h(n) m e(n) x(n)
• x(n)T x(n)

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ANC CONFIGURATION

S
Reference Noise
-
Adaptive Filter
Input With Noise
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ANC CONFIGURATION

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

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ANC IMPLEMENTATION
Reference Noise Seismometer
Signal Seismometers
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ALE CONFIGURATION

Reference Noise
S
-
t
Adaptive Filter
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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 Widrows LMS Adaptive Filter
• Filter Output Signal Is Recovered (Denoised)
  Signal

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ALE CONFIGURATION

• Sample of Noisy Signal

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ALE CONFIGURATION

• Recovered Signal Using ALE

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ALE IMPLEMENTATION

• Example of Noise and Tone on a Speech Segment

Speech With Tone Cleaned Speech Speech With
Noise Cleaned Speech
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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

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FAST FOURIER TRANSFORM

• Noisy Signal

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FAST FOURIER TRANSFORM

• Fast Fourier Transform Of Noisy Signal

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FAST FOURIER TRANSFORM

• Fast Fourier Transform After Coefficient Shrinkage

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FAST FOURIER TRANSFORM

• Recovered Signal Using Coefficient Shrinkage

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WAVELET DECOMPOSITION

• Special Orthogonal High Pass And Low Pass Filters
• Down Sample By 2
• Up Sample By 2

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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

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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

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COEFFICIENT SHRINKAGE

• Original Recorded Signal

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COEFFICIENT SHRINKAGE

• Recovered Signal With FFT Decomposition Alone

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COEFFICIENT SHRINKAGE

• Pulse Is Good Signal For DWT Decomposition

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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

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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)

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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
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SIGNAL DECOMPOSITION

• Alternate Filter Bank Method

S
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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

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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

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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

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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
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FREQUENCY SAMPLING FILTER

• FSF Comprises Two Basis Blocks
• Comb Filter
• Resonator

FSF
Comb Filter
Resonator
C(z)
Rk(z)
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COMB FILTER

• Block Diagram

S
x(n)
Z-N
rN
u(n)
-

• Comb Filter Not Necessary For Implementation

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Resonator
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RESONATOR

• Block Diagram

u(n)
Z-1
-
r cos(qk)
S
S
y(n)
-
r2
Z-1
2
Z-1
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GOOGLE RESONATOR SEARCH
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VOICE ACTIVITY DETECTOR

• Calculate Power In A Formant (Usually First)

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DECISION LOGIC

• Speech Present Based On Inequality

• Gain Based On Inequality

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GAIN MODIFICATION

• Gain Factor Requires Post-Emphasis

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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

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EXAMPLE

• Recording From Live Cellular Traffic

• Original Noisy Sample
• After Noise Reduction
• Original Noisy Sample
• After Noise Reduction

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QUESTIONS?