The study of brain network connectivity as a time-varying property began relatively recently and to date has remained primarily concerned with capturing a handful of discrete static states that characterize connectivity as measured on a timescale shorter than that of the full scan. Capturing representations of temporally evolving patterns of connectivity is a challenging and important next step in fully leveraging the information available in fMRI data. We introduce a constellation of interrelated data-driven methods that hierarchically employ multichannel 1D sparse convolutional dictionary learning (SCDL) and independent component analysis (ICA) for extracting multiscale time-varying representations of functional network connectivity (FNC). This work also relies upon a novel wavelet-based method for computing dynamically varying FNC (dFNC) at each timepoint in the scan, yielding a much more resolved picture of evolving connectivity than currently popular sliding-window approaches. The methods are validated in application to a large multisite fMRI study of schizophrenia where they expose properties of time-varying connectivity in schizophrenia patients vs. controls that are surprising based on long-accepted theories of the disorder.