This question is related also to that question HERE, but with further details and another issue I need to solve.
Assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is equal to $H(X) = \Re(FFT(X)) - \Im(FFT(X))$. where $H$ denotes the Hartley transformation, and $FFT$ is the discrete Fourier transformation. Which means that $y = H(X)$. My question : Is it possible to fix some values in the vector $X$, for example, $X_{1:4:N}$ to be any values in order to have their correspondent values $y_{1:4:N}$ equal to $[1,1,\ldots,1]?$. What supposed to be the valued of $X_{1:4:N}$ to have the results of $y_{1:4:N}=[1,1,\ldots,1]?$
$NP:$ The values in both vectors $x$ and $y$ in the other index of $1:4:N$ are random data.