I'm trying to understand the following formula in this paper:
Sadly, the paper does not define most of the symbols it is using, so my guesses so far are:
- $T_{tr}$ refers to the sampling interval
- i.e. $\frac{1}{44100} s$
- $\phi$ refers to phase
- specifically: $\phi(k_{tr}, (n-1)h)$ refers to the angle of the complex vector representing frequency $k_{tr}$ for the FFT from time point $(n-1)h$ to $nh$
- so basically this is saying: out of all FFT frequency bins, only include those frequencies $k_{tr}$ where above equation holds true
I tried googling around to see if there's a standard definition of "transient frequency bins" (like there is for FFT frequency bins) this is referencing, but no success. I also don't understand
- Why would one compare radians $\phi$ with a unit of time $T_{tr}$?
- Is this maybe a stand-in for 0 to account for sampling errors?
- Why isn't $T_{tr}$ just called $T$ as it seems to be a property of the signal and unrelated to the transient bins?
- (If this is not the sampling interval, then how would one obtain $T_{tr}$?)
How does this formula define $K_{tr}$?