The generation and propagation of an electromagnetic pulse (EMP) in real time, can be visualized in time domain because of its transient nature. The coupling of an EMP with different systems can be assessed by analyzing the frequency spectrum and can be very well understood in the frequency-domain through the lowest frequency, the highest frequency, and the energy content. This chapter presents the mathematical waveforms representing the nuclear electromagnetic pulse (NEMP) for simulating the electromagnetic environment in the event of nuclear explosion. It discusses most commonly used waveforms of a high-altitude electromagnetic pulse. The characteristics of a NEMP waveform in time-domain can be understood through the following parameters: rise time, pulse duration, and peak characteristics. The transient nature of an EMP is revealed by the time-domain analysis. The frequency domain analysis helps us to understand how does an EMP couples with different systems.