  In this article, we propose a methodology to reconstruct, in a single step,
the mean- and unsteady properties of a flow from very few time-resolved
measurements. The procedure is based on the {\it a priori} alignement of
Fourier- and Resolvent-modes over energetic frequencies, which is a common
feature in shear-dominated transitional flows. Hence, the Reynolds-stresses,
which determine the mean-flow, may be approximated from a series of Resolvent
modes, which discretize the fluctuation field in the frequency space and whose
amplitudes can be tuned thanks to few measurements. In practice, we solve a
nonlinear optimization problem (with only few parameters) based on a model
coupling strongly the equations governing the mean-flow and the Resolvent
modes. The input data for the assimilation procedure may be very sparse,
typically one or two pointwise measurements. This technique is applied to two
distinct physical configurations, one "oscillator" flow with periodic
fluctuations (squared-section cylinder) and one "noise amplifier" flow with a
broadband frequency spectrum (backward-facing step).
