Hi Tim,
Many thanks for the message.
This is what I think. I guess that the word "baseline" is a little bit vague and confusing as well. If there is only a constant value for each voxel as a "baseline" when we model the FMRI signal, we could just use the average value along the time as the t^0 term, and we wouldn't care at all whether there are some windows of fixation, for example, in the experimental design. In other words, as you said, you could have regressors covering all timepoints.
However, most of time the brain seems not staying there with a horizontal line of signal even if it is not performing any tasks. Instead we model the resting state with a seasonal (trend) effect, usually in linear or even quadratic fashion. That is, we fit the resting state with c0 t^0 + c1 t or c0 t^0 + c1 t + c2 t^2. Some people even fit it with higher order of polynomials. With 3dDeconvolve, if you don't specify the "baseline" model when you run 3dDeconvolve, the program assumes that you want a linear fitting of the "baseline" (c0 t^0 + c1 t) instead of constant (c0 t^0). Otherwise the option "-polort #" would tell 3dDeconvolve the order (#) of the fitting polynomial. Exactly for this reason, a good experiment design needs some extent (usually 15-40%) of the scanning time devoted specifically for resting (control) state so that we could model the "baseline" (polynomial) part.
Does this make sense?
Gang