# MFCC delta: How to compute delta, in real time, with no future frames?

I am trying to compute Delta coefficients for real-time audio analysis. As far as I know, a valid formula is:

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

It seems that I need $n$ future frames at each time step $t$ to compute both delta and delta-delta. However in real-time, I don't have future frames for several $\textrm{ms}$ (depending on my window segmentation). My methodology would be to compute, for timestep $t$, delta and delta-delta with an offset (i.e. compute the values from the previous frame or the one before). But then, these coefficients would correspond to one of the previous frames, bringing an offset to the feature vectors.

Is there any other way to get around this issue ? (maybe using a slightly different formula ?)

In practice first two frames of the feature vector for both $\Delta$ and $\Delta\Delta$'s are zeros. So in fact the coefficients are delayed by two frames. These can be calculated according to the formulas:
$$\Delta[t] = c[t]-c[t-2]$$ $$\Delta\Delta[t] = c[t-2]-2c[t-1] + c[t]$$