How to express this formula?

Please teach me how to write the matlab code for this formula?

[KL]

Here: https://www.mathworks.com/help/matlab/getting-started-with-matlab.html

Answer 1

[Walter Roberson]

In MATLAB it is written as fft(X) /sqrt(length(X)) it appears to me.

[Alex Phang]

Can I know what is the equation for fft(X)? How can the equation after sigma ∑ is fft(X)? I read from Fast Fourier transform and it explains a little different. How to change the top and the bottom of the sigma ∑ in the fft?

[Walter Roberson]

https://en.wikipedia.org/wiki/Fast_Fourier_transform#Definition_and_speed

[Alex Phang]

What about expression like this? How to express the sigma ∑?

[Walter Roberson]

Calculate the terms of what goes inside the inner sigma as a vector. sum() the vector. However, you cannot do that for the outer infinite sigma.

For the outer infinite sigma, you would use symsum() . I tend to doubt you will get a closed-form formula however.

I suspect for that equation you need to somehow decompose the formula as a convolution. Maybe you could get somewhere with a Z Transform or Laplace Transform.