# Phase Estimation in speech enhancement

I am reading a recent paper titled "Phase Estimation of Speech Enhancement - unimportant, important, or impossible?" by Grekmann et al. published in the 2012 the IEEE convention. The paper proposes an algorithm for estimating the phase of the noisy speech.

can anyone help me please on understanding what is meant by "angular frequency of the harmonic component dominant in band k" ?

Thanks in advance

• Presumably, there exists one or more harmonics in each band specified and therefore whichever frequency the one with the most spectral energy occurs at. Note that based on the variables used, it is likely to be the normalised frequency rather than actual. Dec 15, 2014 at 8:08
• For those who are interested, I found a better paper about phase estimation. It is for the same author, but different publications. It is in the: M. Krawczyk and T. Gerkmann, “STFT phase improvement for single channel speech enhancement”, International Workshop on Acoustic Signal Enhancement, 2012.
– Mona
Dec 16, 2014 at 19:01

## 1 Answer

According to their model given by Eq. (2), voiced speech is assumed to consist of a weighted sum of sinusoids with frequencies that are multiples of the fundamental frequency. They assume that in each frequency band $k$ there is one dominant harmonic with normalized angular frequency $\Omega_h^k$, which is the harmonic that is closest to the frequency corresponding to the $k^{th}$ frequency bin of the FFT. The frequency of this harmonic is used to estimate the current phase in band $k$ from the previous phase value in that band according to Eq. (3).

• Thank you very much. This is very clear, but we can never know the fundamental frequency, f0. I will continue reading the rest of the paper, maybe we don't need to find f0. Thanks again
– Mona
Dec 16, 2014 at 1:15
• well, since it may not even be the fundamental that is dominant for that FFT band (or should it be "bin" or "all of the bins in the band"), you really need to independently identify the frequency component with dominant energy in that bin or band. for the phase vocoder, we sorta take that equation (3) in reverse, and compute a frequency to greater precision than the FFT bin width by noticing how much the phase has advanced from one frame (or "segment") to the next. Dec 16, 2014 at 20:26