Abstract: One of the main objectives of a radiation spectroscopy is to have good energy resolution so that the results of the nuclear physics experiments can be interpreted faithfully. Electronic noise introduced by the instrumentation systems put a major constraint on the energy resolution. It has been proved theoretically by many researchers/authors that the signal to noise ratio can be maximized to its best value if the electrical pulse obtained from a nuclear detector can be shaped into an infinite cusp form. Practically a cusp-like pulse of finite length can be obtained by processing the detector signals in digital domain. This paper considers VHSIC Hardware Description Language (VHDL) simulation aspect of cusp-like filtering algorithm. Such simulations provide the platform to verify the algorithms for their implementation into a digital hardware such as Field Programmable Gate Array (FPGA) for real time applications. The simulation considers exponentially decaying sequences as the input to the filter. In radiation spectroscopy applications, such signals are obtained by digitizing the slow decaying exponential pulses derived from radiation detectors.