Length of Hamming Window to Resolve a Harmonic

1. What is the formula for Hamming window?
2. What is the purpose of Hamming window?
3. Why the use of Hamming window can reduce the problem of using rectangular window?

What is the formula for Hamming window?

The following equation generates the coefficients of a Hamming window: w ( n ) = 0.54 − 0.46 cos ( 2 π n N ) , 0 ≤ n ≤ N .

What is the purpose of Hamming window?

In particular, a Hamming window will reduce the size of the first Sinc side lobe of "leakage" right next to the frequency peak in exchange for actually more "leakage" (or convolution splatter) far from the frequency of interest. Other windows may be more appropriate if you wish a different trade-off.

Why the use of Hamming window can reduce the problem of using rectangular window?

By using a window function other than the rectangular one there is less of the sidelobes compared to the main lobe, so less artificial long-distance spread making the result cleaner and better suited for frequency-selective analysis.