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Implicit Speaker SeparationPowerPoint Presentation

Implicit Speaker Separation

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### Implicit Speaker Separation

DaimlerChrysler Research and Technology

Reminder on Least-Mean Square (LMS)

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- The filter w2 is adapted with the normalized Least-Mean Square (NLMS) algorithm.
w2(n+1) (k) = w2(n) (k)- m y1(t)x2(t-k)/s2x2

- Converges if the target is not active: speaker activity detection required
- Convergence is assured (in the mean) if
0 <m < 2

Reminder on Least-Mean Square (LMS)

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- NLMS w2(n+1) (k) = w2(n) (k)- m y1(t)x2(t-k)/s2x2
- Adapts slower when the interferer is loud (for stability)

From LMS to “Implicit” LMS

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- NLMS w2(n+1) (k) = w2(n) (k)- m y1(t)x2(t-k)/s2x2
- Adapts slower when the interferer is loud (for the stability)
- Implicit LMS w2(n+1) (k)= w2(n) (k)– m0y1(t)x2(t-k)}/s2y1
- Adapts slower when the target is loud : less target cancellation
- Adapts faster when the output (=target) is weak.
- Adapts… maybe to fast.

“Implicit” LMS stability condition

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- NLMS w2(n+1) (k) = w2(n) (k)- m y1(t)x2(t-k)/s2x2
- ILMSw2(n+1) (k)= w2(n) (k)– m0y1(t)x2(t-k)2/s2y1
- ILMS = NLMS with time varying step size
m (k) = m0s2x2 /s2y1

- ILMS stability condion: 0 < m (k)< 2
0 < m0s2x2 /s2y1 < 2

“Implicit” LMS stability condition

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- ILMS stability condition:
- 0 < m0s2x2 /s2y1 < 2
- Fulfilled ? If yes then
w2(n+1) (k)= w2(n) (k)– m0y1(t)x2(t-k)2/s2y1

If not then NLMS with step-size m0

w2(n+1) (k) = w2(n) (k)- m0y1(t)x2(t-k)/s2x2

“Implicit” LMS stability condition

x1 (signal ref)

+

y1 = x1 + x2* w2

w2

x2 (noise ref)

- ILMS stability condition:
- 0 < m0s2x2 /s2y1 < 2
- Fulfilled ? If yes then
w2(n+1) (k)= w2(n) (k)– m0y1(t)x2(t-k)2/s2y1

If not then NLMS with step-size m0

w2(n+1) (k) = w2(n) (k)- m0y1(t)x2(t-k)/s2x2

When does it happen ?

“Implicit” LMS stability condition

- We describe the system with
- emismatch = “how far is w2 from optimum”
- eleakage = “how much driver speech is received in codriver microphone”
- ILMS stability condition: 0 < m0s2x2 /s2y1 < 2
- is not fulfilled if and only if
- (i) means: “we are close to optimum”
- (ii) means: “the driver is weak with respect to codriver”
- => NLMS normalization is convenient.

Replace the noise reference x2 with the best available reference y2.

No adaption control needed (blind).

High complexity w.r.t. NLMS or ILMS

From ILMS to BSS (Blind Source Separation)Dependence measure

w1 and w2 are jointly optimized such that the outputs are independent.

x1

+

y1

w1

w2

ILMS (reminder)

+

y2

w2(n+1) = w2(n) – m y1(t)x2 (t-k)/s2y1

x2

w1(n+1) = w1(n) – my2(t) y1 (t-k)/s2y1

w2(n+1) = w2(n) – my1(t) y2 (t-k)/s2y2

How does it sound ?

- Microphone signals:
- Blocwise adaptation
- Unsupervised NLMS
- Supervised NLMS
- Implicit ILMS
- BSS

- Samplewise adaptation
- Unsupervised NLMS
- Supervised NLMS
- Implicit ILMS

Conclusion

- NLMS
- converge fastest (target silent) and…
- … diverge fastest (double talk).
- 15 dB SIR improvement with perfect double detection

- ILMS
- very robust, no explicit speaker detection
- 10-12 dB SIR improvement
- low compexity

- BSS
- robust and converge fast
- SIR improvement 15 dB
- high complexity

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