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## Main Question or Discussion Point

I'm currently carrying out an analysis on waveforms produced by a particular particle detector. The Nyquist-Shannon sampling theorem has been very useful for making an interpolation over the original sample points obtained from the oscilloscope. The theorem (for a finite set of samples) is given by:

$$x(t) = \sum_{n=1}^{N} x(nT)sinc\bigg(\frac{t-nT}{T}\bigg)$$

It seems that it would also be very useful to have a function that can do the opposite operation (i.e. you give it a value of x and get t):

$$t(x)$$

I'm wondering whether or not this can be easily achieved. I'm not sure where to start due to the sum on the RHS. Any help or tips on how to start would be greatly appreciated.

$$x(t) = \sum_{n=1}^{N} x(nT)sinc\bigg(\frac{t-nT}{T}\bigg)$$

It seems that it would also be very useful to have a function that can do the opposite operation (i.e. you give it a value of x and get t):

$$t(x)$$

I'm wondering whether or not this can be easily achieved. I'm not sure where to start due to the sum on the RHS. Any help or tips on how to start would be greatly appreciated.