Finding the close form of the expression containing two summations
I am trying to deduce an equation and right now I am stuck at a point where there are two summations. Below is the equation where I am stuck. Kindly, help to deuce this further to obtain a closed form expression. Else, how to convert this in matrix form? Any help is appreciated. Thanks in advance.
$R(n,epsilon)=frac{1}{N^2} exp(frac{jpi n^2}{Nm}) sum_{d=0}^{N-1} sum_{g=0}^{N-1} exp (frac{jpi md^2}{N}) exp(frac{-jpi m (g-n)^2}{N}) (frac{1-exp(j2pi epsilon)}{1- exp(frac{j2pi(epsilon +d-g)}{N})}) $
matrices summation closed-form exponential-sum
asked Dec 11 '18 at 4:23
Saquib Khan
12
add a comment |
I am trying to deduce an equation and right now I am stuck at a point where there are two summations. Below is the equation where I am stuck. Kindly, help to deuce this further to obtain a closed form expression. Else, how to convert this in matrix form? Any help is appreciated. Thanks in advance.
$R(n,epsilon)=frac{1}{N^2} exp(frac{jpi n^2}{Nm}) sum_{d=0}^{N-1} sum_{g=0}^{N-1} exp (frac{jpi md^2}{N}) exp(frac{-jpi m (g-n)^2}{N}) (frac{1-exp(j2pi epsilon)}{1- exp(frac{j2pi(epsilon +d-g)}{N})}) $
matrices summation closed-form exponential-sum
asked Dec 11 '18 at 4:23
Saquib Khan
12
add a comment |
I am trying to deduce an equation and right now I am stuck at a point where there are two summations. Below is the equation where I am stuck. Kindly, help to deuce this further to obtain a closed form expression. Else, how to convert this in matrix form? Any help is appreciated. Thanks in advance.
$R(n,epsilon)=frac{1}{N^2} exp(frac{jpi n^2}{Nm}) sum_{d=0}^{N-1} sum_{g=0}^{N-1} exp (frac{jpi md^2}{N}) exp(frac{-jpi m (g-n)^2}{N}) (frac{1-exp(j2pi epsilon)}{1- exp(frac{j2pi(epsilon +d-g)}{N})}) $
matrices summation closed-form exponential-sum
asked Dec 11 '18 at 4:23
Saquib Khan
12
I am trying to deduce an equation and right now I am stuck at a point where there are two summations. Below is the equation where I am stuck. Kindly, help to deuce this further to obtain a closed form expression. Else, how to convert this in matrix form? Any help is appreciated. Thanks in advance.
$R(n,epsilon)=frac{1}{N^2} exp(frac{jpi n^2}{Nm}) sum_{d=0}^{N-1} sum_{g=0}^{N-1} exp (frac{jpi md^2}{N}) exp(frac{-jpi m (g-n)^2}{N}) (frac{1-exp(j2pi epsilon)}{1- exp(frac{j2pi(epsilon +d-g)}{N})}) $
matrices summation closed-form exponential-sum
matrices summation closed-form exponential-sum
asked Dec 11 '18 at 4:23
Saquib Khan
12
asked Dec 11 '18 at 4:23
Saquib Khan
12
edited Dec 11 '18 at 4:37
asked Dec 11 '18 at 4:23
Saquib Khan
12
asked Dec 11 '18 at 4:23
Saquib Khan
12
asked Dec 11 '18 at 4:23
Saquib Khan
12
12
add a comment |
add a comment |
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