I am currently reading a paper about speech enhancement. The paper uses Spectral Subtraction Method. On that section, The paper stated that ω is the "discrete angular frequency index of the frames"

Question: What is the discrete angular frequency index? Is it part of Short Time Fourier Transform?

Assume that the noisy speech $\boldsymbol{y[n]}$ can be expressed as $\boldsymbol{y[n] = s[n] + d[n]}$, where $\boldsymbol{s[n]}$ is the clean speech and $\boldsymbol{d[n]}$ is the additive noise. As the enhancement is carried out according to the frame, the above model can be expressed as $$y(n,k) = s(n,k) + d(n,k),\quad n=0,1,2,\ldots,(N-1);\quad k=1,2,\ldots,N\tag{1}$$ Here $n$ is the discrete time index, $k$ is the frame number and $N$ is the length of the frame. $$y(\omega,k) = S(\omega,k) + D(\omega,k)\tag{2}$$ Here $\omega$ is the discrete angular frequency index of the frames.

The paper is:

Navneet Upadhyay and Rahul Kumar Jaiswal: "Single Channel Speech Enhancement: Using Wiener Filtering with Recursive Noise Estimation", Procedia Computer Science, Volume 84, 2016, Pages 22-30, doi:10.1016/j.procs.2016.04.061.


$\omega$ is angular frequency in radians, $\omega =2\pi fT$, where $f$ is frequency (for example in Hz) and $T$ is sampling period (for example in seconds). This is revealed by Eq. 3:

$$Y(\omega, k) = \textstyle\sum_{n=-\infty}^\infty y(n)w(k-n)e^{-j\omega n}\tag{3},$$

which represents discrete-time Fourier transform (DTFT) of windowed signal $y(n)w(k-n)$.

It's not common to call $\omega$ "discrete angular frequency index", which gives just 3 google hits.

  • $\begingroup$ I see. But I never heard of DTFT function exist in python especially Librosa, do you have any reference on how I compute in Python? Moreover, the paper also mentions that they use STFT in Fig.2 is STFT is the same with STFT? $\endgroup$ Apr 26 '19 at 9:53
  • $\begingroup$ @AndreasChandra sorry, I only wanted to answer the specific question. $\endgroup$ Apr 26 '19 at 10:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.