MFCC Deltas, Delta-Deltas

Question

I have just a quick question about how to calculate Deltas from MFCC. I have found the formula for calculating deltas here:

$$d_t=\frac{\sum_{n=1}^{N}n\left(c_{t+n}-c_{t-n}\right)}{2\sum_{n=1}^{N}n^2}$$

Another source states it is a regression equation. From what I can see, it takes coefficient from a previous and next frame. For any $N$ e.g. $N=2$, $t-n$ in $c_{t-n}$ can refer to the past where there are no frames. Which values should I substitute in this case? Should it be simply 0?

Similarly, when $t+n$ in $c_{t+n}$ refers to a frame in future that not exists, should it also be 0?

Thanks

Answer 1

It's better to copy first frame and last frame values to extend vector sequence beyond boundaries than to assign 0. This could be implemented just by adjusting indexes:

if (index1 < 0)
    index1 = 0
if (index2 > N - 1)
   index2 = N - 1

delta = v[index1] - v[index2]