I am completing Fourier analysis on many different time series of sediment particle flux exiting an experimental flume. Data is collected at a resolution of 1 Hz for durations ranging from ~5,000 to 50,000 seconds. Flux ranges from 0 to over 1,000 particles. The figure below shows an example time series that I am analyzing - the x-axis has units of seconds and the y-axis has units of particles/second:
I am familiar with time series and Fourier analyses, but I am not an expert. A colleague told me that I should detrend all of my time series before performing the Fourier analysis. I have completed the analysis without, and with detrending the time series and I see no obvious difference in the resultant spectra; this does not surprise me because I see no secular trend, for example, in the data shown in the example figure above. This leaves me with several questions. First, should I detrend the example time series shown in the figure above? If I should, why (or why not)? Second, there are at least several ways I can think of to detrend the example time series (e.g. subtracting a polynomial fit, subtracting the series mean, etc.), do people have any suggestions for a time series like the example one shown above? Last, are there clear criteria I can work with in making a decision of whether detrending is necessary prior to completing a Fourier analysis? Thanks.