I use the MSP430FR2355 microcontroller and the display connected to it. I create 2 arrays with time and voltage values, a graph is plotted on the display based on these values. After that, I pass these values to the dac register. how can I do sinc interpolation for these values to get a smooth graph? Is it possible to use the hamming window function for this? Another clarification is that the microcontroller does not support floating point.
Or I can make a table of coefficients of the hamming window function and multiply my values by this table, will it work?
You shouldn't need to use sinc interpolation.
If your signal is properly sampled to begin with, then the original signal contains no frequencies >= Fs/2. In practice, you want to leave a little headroom. If the original signal has no frequencies over Fs x 0.4, for example, then the anti-aliasing filter you need to apply to get a "smooth signal" is much gentler and shorter.
If your DAC supports a higher sampling frequency than you already have, then you should up-sample to the DAC's sampling rate and then apply a digital FIR filter to do most of the anti-aliasing work digitally. This is known as "oversampling".
Regardless, the final anti-aliasing filter should be an analog filter applied to the DAC output. Again, the further your signal is away from Fs/2, the simpler this is. If your signal originally goes up to Fs x 0.4, for example, and you use 2x oversampling, then the DAC output will only have frequencies up to Fs x 0.2, and the analog filter can be very simple. It only has to pass frequencies less than Fs x 0.2 and cut off frequencies greater than Fs x 0.8.