Detrend data with no clear secular trend prior to Fourier analysis? 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.
How you pre-process data is related to the purpose of the analysis and since you haven't mentioned why you are doing spectral analysis, answering your question can't go beyond making some general remarks.

Detrending is a preprocessing operation. You want to compensate or remove some bias from your data. As an example, many kinds of data are collected in the presence of long term phenomena that is extraneous to what your are interested in finding. Many kinds of data have seasonal, diurnal, weekly, monthly, tidal, .... ect cycles associated with them. Unemployment has a seasonal dependence to it as an example.

I once was tasked with looking for jumps in syndrome data that is reported to health departments and there was strong increases on Mondays and after holidays in reports but that had to do with many doctor's offices being closed on weekends.  This was an artifact of how the data is collected and not how epidemics evolve.

Matlab's dtrend function removes a linear fit from data.  If the collection interval is small compared to some much longer trend in the data, it reduces the bias introduced by taking a section that is less than the period of the longer term trend, particularly for data like your which is strictly positive.  One may conceptualize dtrending as reducing low frequency spectral leakage that would otherwise mask features in your spectra.

Again, without knowing what you are looking for in your data, no specific answer can be recomended for your situation.