Given a smooth function with only jump discontinuities on the interval \((0,1)\) (and possibly on its boundary when extended periodically). The problem is to find the jumps, given its Fourier coefficients \(\hat{f}(k)\), \(|k|\leq N\). The convolution \(f*K_N\) of \(f\) with a concentration kernel \(K_n\) will remove the smooth part and isolate the jumps while Gibbs oscillations are suppressed as much as possible (see e.g.[E. Tadmor, Acta Numerica 16, 305–378 (2007; Zbl 1125.65122)]). The authors propose a concentrated kernel that results in a mollified Fourier sum \[ T_N[\sigma_\lambda](x)=2\pi i\sum_{|k|\leq N}n\widehat{\sigma_\lambda}(n)\hat{f}(n)e^{2\pi i nx} \] where \(\sigma_\lambda(x)=\sigma(\lambda x)\) and \(\sigma\) is a function from a suitable class. For \(\lambda\) going to infinity with \(N\), it is shown that \(T_N[\sigma_\lambda](x)\) will converge to the jumps. Some numerical examples illustrate the robustness and convergence of this edge detection method in the presence of noise and for jumps in close proximity.