The classical Shannon sampling theorem applies exclusively to bandlimited signals. This paper extends the theory to a class of non-bandlimited signals that still permit exact uniform sampling. We introduce a ladder-shaped filter with m real parameters, whose impulse response is a generalized Sinc function obtained from finite Blaschke products. For the corresponding signal space, we establish a generalized sampling theorem that reconstructs any signal from its samples {f(nπ/Ω)}n∈Z using the multi-parameter generalized Sinc kernel. Additionally, we prove that these signals can be analytically extended to a strip in the complex plane, generalizing the Paley–Wiener theorem to the non-bandlimited setting. The proposed framework bridges the gap between classical bandlimited theory and practical non-bandlimited signals, providing both theoretical foundations and tools for signal processing applications.