Sampling Theorem: How to know the value between two samples of a Signal According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited).

Let's say, we have a signal with f= 2MHz (highest freq component), so we will be sampling it at 4MHz or more as Sampling theorem say's.. and we will have N Samples in signal.

Now, what if I want to know the exact value of a sample (information) between two samples..??

How can we find the value at every possible instantaneous.. in a signal..when we know we only have N samples after sampling..??

I know we can increasing sampling rate to have more sample. But is there any other way to do it..?

This question was asked to me in an interview at NCRA-TIFR, Pune, India.
Interpolation using a Sinc function kernel.  This assumes that the sampled signal was perfectly bandlimited to below half the sampling rate.

Note that perfectly bandlimited signal are infinite in extent.  For finite-length "real world" signals, using a windowed Sinc interpolation kernel (thus a finite computation with a noise floor) is a common method to approximate points between samples (for upsampling, for instance).