On continuous numerical Fourier transform for transient analysis of lightning current related phenomena

• Continuous numerical Fourier transform for use in transient analysis is developed.
• Algorithm is based on finite element technique and linearization of lightning current.
• Transformed function in the frequency domain is continuous, not discrete.
• Any lightning current function can easily be transformed including measured currents.

In this paper a novel numerical method is proposed for solving the Fourier transform of an arbitrary transient function. Fourier integral is solved using a combination of numerical and analytical integration resulting in a continuous transient function in the frequency domain. The proposed numerical algorithm enables robust and accurate transformation of any arbitrary transient function into the frequency domain. This also includes arbitrarily sampled measured lightning currents. The result of the transformation in the frequency domain is continuous and completely independent of the time domain sampling procedure unlike in transformation algorithms that are generally employed for this purpose. Accuracy of the proposed algorithm has been verified on a number of numerical examples.