Time Difference of Arrival Estimation of Speech Source in a Noisy ...

EE049035 – Spring 2007
Spectrum Analysis
Using that the speech and noise are uncorrelated
we get the PSD:
* *
z z i j ss i j nn
Φ ( w) = A( w) A ( w) Φ ( w) + B ( w) B ( w) Φ ( w)
i j
The connection between ( ) and Φ ( ) :
Φzmz w 1 1 1
Φ − Φ = Φ
( w) H ( w) ( w) 1 ( w)
m 1 1 1
m
z z m z z b
where 1 ( ) is a noise only term:
Φ
b w
m
z z w
2
bm
m m 1 nn
Φ 1 ( w) = ( G ( w) − H ( w) ) B ( w) Φ ( w);
G ( w)
≜
m
Bm( w)
B ( w)
Problem – speech is non stationary - Φss(
w)
1
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