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The fundamentals of Fourier Transform are presented, with analyticalsolutions derived for Continuous Fourier Transform (CFT) of truncated signals,to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFTwere identified for decay curves. An existing method for Infrared Thermography,Pulse Phase Thermography (PPT), was benchmarked against a proposed method usingpolynomial fitting with CFT, to analyse cooling curves for defectidentification in Non-Destructive Testing (NDT). Existing FFT methods used inPPT were shown to be dependent on sampling rates, with inherent artifacts andinconsistencies in both amplitude and phase. It was shown that the proposedmethod produced consistent amplitude and phase, with no artifacts, as long asthe start of the cooling curves are sufficiently represented. It is hoped thata collaborative approach will be adopted to unify data in Thermography formachine learning models to thrive, in order to facilitate automated geometryand defect recognition and move the field forward.

Continuous Fourier Transform: A practical approach for truncated signals and suggestions for improvements in thermography