# What is discrete angular frequency?

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.