The `hrf_mexhat` function computes the Mexican hat wavelet-based HRF (hemodynamic response function) at given time points `t`.
Details
The response is the Ricker (Mexican hat) wavelet centred at
mean with width sd, set to zero before onset (t < 0):
$$h(t) = \frac{2}{\sqrt{3\,sd}\,\pi^{1/4}}
\left(1 - \left(\frac{t - mean}{sd}\right)^2\right)
\exp\left(-\frac{(t - mean)^2}{2\,sd^2}\right).$$
The normalising constant gives the un-truncated wavelet unit L2 norm.
See also
Other hrf_functions:
hrf_basis_lwu(),
hrf_boxcar(),
hrf_bspline(),
hrf_gamma(),
hrf_gaussian(),
hrf_inv_logit(),
hrf_lwu(),
hrf_sine(),
hrf_spmg1(),
hrf_time(),
hrf_weighted()
Examples
# Compute the Mexican hat HRF representation for time points from 0 to 20 with 0.5 increments
hrf_mexhat_vals <- hrf_mexhat(seq(0, 20, by = .5), mean = 6, sd = 2)