A model of the signal path in arterial spin labeling (ASL)-based functional magnetic resonance imaging (fMRI) is presented. Three subtraction-based methods for forming a perfusion estimate are considered and shown to be specific cases of a generalized estimate consisting of a modulator followed by a low pass filter. The performance of the methods is evaluated using the signal model. Contamination of the perfusion estimate by blood oxygenation level dependent contrast (BOLD) is minimized by using either sinc subtraction or surround subtraction for block design experiments and by using pair-wise subtraction for randomized event-related experiments. The subtraction methods all tend to decorrelate the 1/f type low frequency noise often observed in fMRI experiments. Sinc subtraction provides the flattest noise power spectrum at low frequencies, while pair-wise subtraction yields the narrowest autocorrelation function. The formation of BOLD estimates from the ASL data is also considered and perfusion weighting of the estimates is examined using the signal model.