Speech Enhancement - Digital Speech: Coding for Low Bit Rate Communication Systems - page 378

The noise floor factor β contributes to the reduction of musical noise sounds.
It has the effect of converting the narrowband musical noise into a wider
band noise. Although higher β values give less musical noise, if β is set too
high it may result in an increase of the level of other artifacts of residual
noise. The over-subtraction factor, α , is useful for reducing the overall level of
residual noise. Higher α values give lower levels of residual noise. However,
too high α values may cause distortion in perceived speech quality. Through
experiments, it is found that GBSS with ν =

0 . 1give
a moderate level of musical noise reduction while maintaining the perceived
speech quality.
In GBSS, both spectral over-subtraction and floor factors are fixed to
constant values. However, each set of parameters exhibits different noise
reduction performances depending on the selection of these two factors. There
are approaches to obtain the optimal factors based on the psycho-acoustic
model and a parametric formulation. In the psycho-acoustic approach, both α
and β change each frame depending on the psychoacousticmasking threshold
for each spectral component [12]. In the parametric formulation, α is derived
using the MMSE-based metric [13].

2, α = 4 ∼ 8, and β =

11.2.2 Maximum-likelihoodSpectralAmplitudeEstimation

= +

InDFT-based speech enhancement, given Y k X k D k ,theoptimumestimate

| |

of the speechmagnitude X k is obtained from the noisy spectrum Y k ,inwhich

=| |

X k exp (jθ k ) where θ k is the phase of X k . Assuming that the noise D k

has complex Gaussian distribution, the probability density function (PDF) of
Y k conditioned over

X k

| X k | and θ k is,

exp

(11.13)

2

Re (e − jθ k Y k )

2

1
πE( |

− |

Y k | − 2 | X k | +| X k |

|| | =

p(Y k X k , θ k )

D k |

2 )

E( | D k |

2 )

McAulay [14] has shown that the maximum likelihood (ML) estimate of | X k |

can be obtained from the derivative of PDF with respect to | X k | ,wherethe

| X k ML estimate | is given by,

2 )

1
2

| X k |= | Y k |+ | Y k |

2

− E( | D k | (11.14)

which can be written in terms of the gain as,

1

1
2 +

1
2

1
γ k

G (ML)
k

= − (11.15)