2004 COMP.DSP CONFERENCE

Survey of Noise Reduction Techniques

Maurice Givens

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

MINIMUM MEAN-SQUARED ERROR

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

• Will Look At LMS

LMS

• Two Types Of Noise Reduction Techniques With LMS

– Adaptive Noise Cancellation (ANC)

– Adaptive Line Enhancement (ALE)

• Similar Configurations h(n+1) = h(n) + e(n) x(n)

x(n)T x(n)

ANC CONFIGURATION

Adaptive Filter

+

-

Input With Noise

Reference Noise

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

ANC IMPLEMENTATION

Signal Seismometers

Reference Noise Seismometer

ALE CONFIGURATION

Adaptive Filter

+Reference Noise -

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

ALE CONFIGURATION

• Sample of Noisy Signal

ALE CONFIGURATION

• Recovered Signal Using ALE

ALE IMPLEMENTATION

• Example of Noise and Tone on a Speech Segment

Speech With Tone

Cleaned Speech

Speech With Noise

Cleaned Speech

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

FAST FOURIER TRANSFORM

• Noisy Signal

FAST FOURIER TRANSFORM

• Fast Fourier Transform Of Noisy Signal

FAST FOURIER TRANSFORM

• Fast Fourier Transform After Coefficient Shrinkage

FAST FOURIER TRANSFORM

• Recovered Signal Using Coefficient Shrinkage

WAVELET DECOMPOSITION

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

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

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

COEFFICIENT SHRINKAGE

• Original Recorded Signal

COEFFICIENT SHRINKAGE

• Recovered Signal With FFT Decomposition Alone

COEFFICIENT SHRINKAGE

• Pulse Is Good Signal For DWT Decomposition

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

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)

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

SIGNAL DECOMPOSITION

• Alternate Filter Bank Method

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

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

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

Noise Cancellation

• Block Diagram

X(n)FSF

VAD

Gk(n)

Y(n)

SIGNAL

POWER

FROM OTHER BANDS

FROM OTHER BANDSNOISE

POWER

COMPUTE

GAIN

TO OTHER BANDS

TO OTHER BANDS

FREQUENCY SAMPLING FILTER

• FSF Comprises Two Basis Blocks– Comb Filter– Resonator

s

kk f

f 2

FSF

Comb Filter Resonator

C(z) Rk(z)

)1(2

)( NN zrN

zC 221

1

)cos(21

)cos(1)(

zrzr

zrzR

k

kk

2

1BW

r

rBW

1

x(n)

• Comb Filter Not Necessary For Implementation

Z-N rN u(n)

COMB FILTER

• Block Diagram

-

Resonator

2211 )cos()2( yzrruzyzuy k

RESONATOR

• Block Diagramu(n)

r2

2

Z-1

r cos(k)

Z-1

Z-1

-

-

y(n)

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VOICE ACTIVITY DETECTOR

• Calculate Power In A Formant (Usually First)

Otherwise

PP

nPnP

nPnPnP

nPnPnP

sn

xmnm

xlnln

xssss

)()1()1(

)()1()1()(

)()1()1()(

PowerNEstimatedP

PowerSpeechEstimatedP

PowerSignalInputP

n

s

x

oise

DECISION LOGIC

• Speech Present Based On Inequality

)()( nPnPIfesentPrSpeech fs

• Gain Based On Inequality

Otherwise

esentPrSpech

nfnP

nfnPnP

klk

xl

ksk

xskx

)()1()1(

)()1()1()(

eechWhen No SpnfnPnP klk

lk ;)()1()1()(

)(

)(1)(

nP

nPnG

kx

k

k

GAIN MODIFICATION

• Gain Factor Requires Post-Emphasis

)(

)(1)(

nP

nPcnG

kx

k

kk

RangeFrequencyighH

RangeFrequencyidM

RangeFrequencyLow

Z

Y

X

ck

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

EXAMPLE

• Recording From Live Cellular Traffic

• Original Noisy Sample

• After Noise Reduction

• Original Noisy Sample• After Noise Reduction

QUESTIONS?