I am wondering whether I can get the upper bound in closed form,






$\sum_n(\alpha \exp(j2\pi n/N))$    where   $\alpha = +1\ or -1$


If alpha is just positive one, this would be just a single value,

but I'm trying to get the upper bound when alpha is +1 or -1, randomly,

while the total amount of +1 and -1 is different at most 1. (N/2 or N/2+1)

I have looked for exponential sums materials, but can't see things like this.  

    
   


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edit : $\alpha $ is generated by LFSR, so it holds pseudo randomness property.  
       or equivalently, it is a maximal length sequences.