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Let $\mathcal R$ denote the generalized Radon transform (GRT), whichintegrates over a family of $N$-dimensional smooth submanifolds $\mathcalS_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcalU\subset\mathbb R^n$ is the image domain. The submanifolds are parametrized bypoints $\tilde y\subset\tilde{\mathcal V}$, where an open set $\tilde{\mathcalV}\subset\mathbb R^n$ is the data domain. The continuous data are $g={\mathcalR} f$, and the reconstruction is $\check f=\mathcal R^*\mathcal B g$. Here$\mathcal R^*$ is a weighted adjoint of $\mathcal R$, and $\mathcal B$ is apseudo-differential operator. We assume that $f$ is a conormal distribution,$\text{supp}(f)\subset\mathcal U$, and its singular support is a smoothhypersurface $\mathcal S\subset\mathcal U$. Discrete data consists of thevalues of $g$ on a lattice $\tilde y^j$ with the step size $O(\epsilon)$. Let$\check f_\epsilon=\mathcal R^*\mathcal B g_\epsilon$ denote the reconstructionobtained by applying the inversion formula to an interpolated discrete data$g_\epsilon(\tilde y)$. Pick a generic pair $(x_0,\tilde y_0)$, where$x_0\in\mathcal S$, and $\mathcal S_{\tilde y_0}$ is tangent to $\mathcal S$ at$x_0$. The main result of the paper is the computation of the limit $$f_0(\check x):=\lim_{\epsilon\to0}\epsilon^\kappa \checkf_\epsilon(x_0+\epsilon\check x). $$ Here $\kappa\ge 0$ is selected based onthe strength of the reconstructed singularity, and $\check x$ is confined to abounded set. The limiting function $f_0(\check x)$, which we call the discretetransition behavior, allows computing the resolution of reconstruction.

Resolution analysis of inverting the generalized $N$-dimensional Radon transform in $\mathbb R^n$ from discrete data