Is there a relatively easy way to detect likely real-time peaks in discrete-time data? Let's say I have a set of data over time, t:

[0, 4, 6, 7, 7, 6, 4, 0]


It seems likely that this data would peak at t=3.5.

Is there a well-known algorithm for calculating this sort of peak?
The most straight-forward solution would be to interpolate the discrete values around the maximum you're interested in, and compute the location of the maximum of the interpolating function. I'd start by using a quadratic or cubic polynomial. This is a simple example of using an interpolating quadratic polynomial.