To Whom It May Concern:

I am new on fMRI from China. Sorry to bother you with some basis questions.

As we know, what any fMRI analysis program does is this: It takes the time series of stimulus onsets, and convolves it with the HRF. This gives a *prediction* of the blood flow response that we should get a given voxel, if that voxel is responding to the stimuli. Then, we take that prediction, and go and compare it against the measured data. And we see how well they match. However, in some other paper, for example Analysis of fMRI Time-Series Revisited from professor J.FRISTON, may use a convolution matrix K see attachment I wonder, does the K matrix used here can represent the HRF convolved? Or, it only represents temporally smooth? If I make sense, if K only means temporally smooth, the X matrix here should be already convolved with HRF. Moreover, I can not find more detail information about the K matrix. I want to know how to represent K in mathematics. All in all, I wonder what K is and how to represent K.

Long time confused with these questions. Really look forward your response.