Wiener Filtering: A linear estimation of clean signal from the noisy signal Using MMSE criterion

Since y and v are zero mean: This is called the time domain Wiener filter

We are looking for a frequency-domain Wiener filter, called the non-causal Wiener filter such that: According to the projection theorem, for the error to be minimum, the difference has to be orthogonal to the noisy input

Popular form of Wiener filter

Spectral Subtraction

MMSE Speech Enhancement We try to optimize the function: g(.) is a function on Rk and

The computation of Eqn1 is generally difficult. For some specific functions, Eqn1 has been derived. For instance, when g(.) is defined to be: Where is the kth coefficient of the DFT of yt , Eqn1 is equivalent to the popular Wiener filter

Automatic Noise Type Selection

Recursive Formula For G:

Nonstationary State HMM

Nonstationary-State HMM

Segmentation Algorithm in NS-HMM

Segmentation Algorithm in NS-HMM

Now we generalize MMSE formulae for NS-HMM