Sometimes it is important to be able to estimate the peak of a sampled continuous function between the samples. This is called subsample peak interpolation and is used in radar, delay estimation, and communication. Typically one fits a model to the sampled data and then finds the maximum of the model. Two models that I have used are parabolas and Gaussian curves. Both have three parameters and can be fit exactly to three samples (even if the samples are not evenly spaced), and, as a bonus, closed form solutions exist for parameters. This package to demonstrate this procedure, including two examples. One demonstrates finding the peak of a function with unevenly spaced samples. The other shows an example of delay estimation to subsample accuracy.
Travis Wiens (2020). Peak Interpolation (https://www.mathworks.com/matlabcentral/fileexchange/24465-peak-interpolation), MATLAB Central File Exchange. Retrieved .