# modalities.fmri.fmristat.hrf¶

## Module: modalities.fmri.fmristat.hrf¶

Computation of the canonical HRF used in fMRIstat, both the 2-term spectral approximation and the Taylor series approximation, to a shifted version of the canonical Glover HRF.

### References¶

Liao, C.H., Worsley, K.J., Poline, J-B., Aston, J.A.D., Duncan, G.H.,
Evans, A.C. (2002). ‘Estimating the delay of the response in fMRI data.’ NeuroImage, 16:593-606.

## Functions¶

nipy.modalities.fmri.fmristat.hrf.spectral_decomposition(hrf2decompose, time=None, delta=None, ncomp=2)

PCA decomposition of symbolic HRF shifted over time

Perform a PCA expansion of a symbolic HRF, time shifted over the values in delta, returning the first ncomp components.

This smooths out the HRF as compared to using a Taylor series approximation.

Parameters: hrf2decompose : sympy expression An expression that can be lambdified as a function of ‘t’. This is the HRF to be expanded in PCA time : None or np.ndarray, optional None gives default value of np.linspace(-15,50,3251) chosen to match fMRIstat implementation. This corresponds to a time interval of 0.02. Presumed to be equally spaced. delta : None or np.ndarray, optional None results in default value of np.arange(-4.5, 4.6, 0.1) chosen to match fMRIstat implementation. ncomp : int, optional Number of principal components to retain. hrf : [sympy expressions] A sequence length ncomp of symbolic HRFs that are the principal components. approx : TODO
nipy.modalities.fmri.fmristat.hrf.taylor_approx(hrf2decompose, time=None, delta=None)

A Taylor series approximation of an HRF shifted by times delta

Returns original HRF and gradient of HRF

Parameters: hrf2decompose : sympy expression An expression that can be lambdified as a function of ‘t’. This is the HRF to be expanded in PCA time : None or np.ndarray, optional None gives default value of np.linspace(-15,50,3251) chosen to match fMRIstat implementation. This corresponds to a time interval of 0.02. Presumed to be equally spaced. delta : None or np.ndarray, optional None results in default value of np.arange(-4.5, 4.6, 0.1) chosen to match fMRIstat implementation. hrf : [sympy expressions] Sequence length 2 comprising (hrf2decompose, dhrf) where dhrf is the first derivative of hrf2decompose. approx : TODO

References

Liao, C.H., Worsley, K.J., Poline, J-B., Aston, J.A.D., Duncan, G.H., Evans, A.C. (2002). ‘Estimating the delay of the response in fMRI data.’ NeuroImage, 16:593-606.