As you know that Discrete Hartley transformation is related to the discrete Fourier transformation, $i.e$, assuming we have a vector $X = [x_0,x_1,\ldots,x_N]$, its Hartley transformation is equal to $H(X) = Real(FFT(X)) - Imag(FFT(X))$. where $H$ denotes the Hartley transformation.
I wonder, if I want the output of the Hartley transformation equals to a vector of length $N$ whose all elements are $1$, it means $H(X) = [1,1,\ldots,1] $, what supposed to be the input $X$? I means I need to formulate the relationship between the inputs and outputs.