In the present paper, we analyze the behavior of the exponential-type generalized sampling Kantorovich operators (Formula presented.) when discontinuous signals are considered. We present a proposition for the series (Formula presented.), and we prove using this proposition certain approximation theorems for discontinuous functions. Furthermore, we give several examples of kernels satisfying the assumptions of the present theory. Finally, some numerical computations are performed to verify the approximation of discontinuous functions (Formula presented.) by (Formula presented.).