def fir(timeseries, design):
"""
Calculate the FIR (finite impulse response) HRF, according to [Burock2000]_
Parameters
----------
timeseries : float array
timeseries data
design : int array
This is a design matrix. It has to have shape = (number
of TRS, number of conditions * length of HRF)
The form of the matrix is:
A B C ...
where A is a (number of TRs) x (length of HRF) matrix with a unity
matrix placed with its top left corner placed in each TR in which
event of type A occured in the design. B is the equivalent for
events of type B, etc.
Returns
-------
HRF: float array
HRF is a numpy array of 1X(length of HRF * number of conditions)
with the HRFs for the different conditions concatenated. This is an
estimate of the linear filters between the time-series and the events
described in design.
Notes
-----
Implements equation 4 in Burock(2000):
.. math::
\hat{h} = (X^T X)^{-1} X^T y
M.A. Burock and A.M.Dale (2000). Estimation and Detection of Event-Related
fMRI Signals with Temporally Correlated Noise: A Statistically Efficient
and Unbiased Approach. Human Brain Mapping, 11:249-260
"""
X = np.matrix(design)
y = np.matrix(timeseries)
h = np.array(linalg.pinv(X.T * X) * X.T * y.T)
return h
def fir(timeseries, design):
"""
Calculate the FIR (finite impulse response) HRF, according to [Burock2000]_
Parameters
----------
timeseries : float array
timeseries data
design : int array
This is a design matrix. It has to have shape = (number
of TRS, number of conditions * length of HRF)
The form of the matrix is:
A B C ...
where A is a (number of TRs) x (length of HRF) matrix with a unity
matrix placed with its top left corner placed in each TR in which
event of type A occured in the design. B is the equivalent for
events of type B, etc.
Returns
-------
HRF: float array
HRF is a numpy array of 1X(length of HRF * number of conditions)
with the HRFs for the different conditions concatenated. This is an
estimate of the linear filters between the time-series and the events
described in design.
Notes
-----
Implements equation 4 in Burock(2000):
.. math::
\hat{h} = (X^T X)^{-1} X^T y
M.A. Burock and A.M.Dale (2000). Estimation and Detection of Event-Related
fMRI Signals with Temporally Correlated Noise: A Statistically Efficient
and Unbiased Approach. Human Brain Mapping, 11:249-260
"""
X = np.matrix(design)
y = np.matrix(timeseries)
h = np.array(linalg.pinv(X.T * X) * X.T * y.T)
return h