1 Speech Enhancement

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

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

9 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

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12 Popular form of Wiener filter

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14 Spectral Subtraction

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19 MAP Speech Enhancement

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

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26 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 y t, Eqn1 is equivalent to the popular Wiener filter

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28 Recursive Formula For G:

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40 Automatic Noise Type Selection

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43 Nonstationary State HMM

44 Nonstationary-State HMM

45 Segmentation Algorithm in NS-HMM

46 Segmentation Algorithm in NS-HMM

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49 Now we generalize MMSE formulae for NS-HMM

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