From the Modulating Function Method to Observers

State estimation is a long-standing problem in the control community and is usually addressed with observers. However, other techniques can also be used to perform estimation. Among such techniques is the modulating function method, which has been used for parameter and state estimation, as well as fault detection, of linear, nonlinear, distributed, and fractional order systems. This letter puts into perspective these two techniques by showing that, for linear systems, observers found in the literature, some of which being standard techniques, can be expressed within a framework defined by the modulating function method, thus showing a new connection between the modulating function method and observers.