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Onset Detectionjason a. hockman A tutorial onA tutorial on

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak PickingDefinitions Preprocessing Reduction ComparisonPeak Picking

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak Picking

transientonset

attack

Definitions

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak Picking

input signalinput signal

processed signal

processed signal

detectionfunction

detectionfunction

onsetlocalization

onsetlocalization

preprocessing

reduction

peak-picking

Definitions

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak PickingPreprocessing

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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g1

g0

x1(n)

g1 x2(n)

g0 g1 x3(n)

g0 x4(n)

original signal

11-22kHz

5.5-11kHz

2.7-5.5kHz

0-2.7kHz

Preprocessing

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak Picking

transient

Preprocessing

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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steady-state

Preprocessing

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak PickingReduction

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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Definitions Preprocessing Reduction Comparison Peak Picking

half-wave rectification

Reduction

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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enveloping

Eo (n)=1N

x(n+ m) win(m)m=−

N2

N2

∑

Reduction

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enveloping

Eo (n)=1N

x(n+ m)[ ]2 win(m)

m=−N2

N2

∑

Reduction

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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magnitude

frequencybins

X(k)

Reduction

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Xk (n)= x(nh+ m)win(m)e−2 jπmk

N

m=−N2

N2

−1

∑ STFT

Reduction

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Xk (n)= x(nh+ m)win(m)e−2 jπmk

N

m=−N2

N2

−1

∑

%E(n)=1N

Wk Xk(n) 2

m=−N2

N2

−1

∑

STFT

HFC

frequencyweighting

Reduction

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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spectral difference method

present magnitude previous magnitude{ }

2−

Reduction

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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phase-based approaches

phase

0π2π

3

2π

π2

ϕ n−2,k

ϕ n−1,k

ϕ n,k

ϕ̂ n,k

Δϕ n,k

(n-1)h(n-2)h (n)h

Reduction

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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ϕ n−2,k

ϕ n−1,k

ϕ n,k

ϕ̂ n,k

(n-1)h(n-2)h (n)h

? 0

≈0

transient

steady-state

Δϕ n,k

Reduction

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ϕ n−2,k

ϕ n−1,k

ϕ n,k

(n-1)h(n-2)h (n)h

Δϕ n,k = ϕ k (n) − 2ϕ k (n −1)+ϕ k (n − 2)

ϕ̂ n,k

Reduction

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−2 X̂k (n) Xk (n) cos(Δϕ k (n))}1

2

Γk (n) = X̂k (n)2+ Xk (n)

2

{

complex domain approach

Reduction

Onset DetectionOnset Detection

University of Montreal > IFT6080 Machine Learning > Onset Detection

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−2 X̂k (n) Xk (n) cos(Δϕ k (n))}1

2

Γk (n) = X̂k (n)2+ Xk (n)

2

{

complex domain approach

phase part

present mag

Xk (n−1)−Xk(n−2)

Reduction

Onset DetectionOnset Detection

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ζ n( ) = Γ k (n)k=1

N

∑

complex domain approach

*sum across k-bins

Reduction

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κ s i[ ] = 2 js d j ,k( j ,k )∈Β i[ ]∑

wavelet method

large value = noisy

wavelet coefficients

Reduction

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University of Montreal > IFT6080 Machine Learning > Onset Detection

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poppianoviolin

Comparison

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satisfies:1. df(n) > df(n-1)2. df(n) > df(n+1)3. df(n) > thresh

local maxima

Peak Picking

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δ t (m) = δ +medianη(km)

adaptive thresholding

km ∈ m−H2

,m+H2

⎡⎣⎢

⎤⎦⎥

Peak Picking

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δ t (m) = δ +medianη(km)

adaptive thresholding

Peak Picking

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…sound examples…