  We generalize the local model of primordial non-Gaussianity by promoting the
parameter fNL to a general scale-dependent function fNL(k). We calculate the
resulting bispectrum and the effect on the bias of dark matter halos, and thus
the extent to which fNL(k) can be measured from the large-scale structure
observations. By calculating the principal components of fNL(k), we identify
scales where this form of non-Gaussianity is best constrained and estimate the
overlap with previously studied local and equilateral non-Gaussian models.
