This paper introduces a recent innovation in dealing with non-periodic behavior often referred to as transients in perturbative experiments. These transients can be the result from the unforced response due to the initial condition and other slow trends in the measurement data and are a source of error when performing and interpreting Fourier spectra. Fourier analysis is particularly relevant in system identification used to build feedback controllers and the analysis of various pulsed experiments such as heat pulse propagation studies. The basic idea behind the methodology is that transients are continuous complex-valued smooth functions in the Fourier domain which can be estimated from the Fourier data. Then, these smooth functions can be subtracted from the data such that only periodic components are retained. The merit of the approach is shown in two experimental examples, i.e. heat pulse propagation (core transport analysis) and radiation front movement due to gas puffing in the divertor. The examples show that the quality of the data is significantly improved such that it allows for new interpretation of the results even for non-ideal measurements.