  This paper is a contribution to the old problem of representing a signal in
the coordinates of time and frequency. As the starting point, we abandon
Gabor's complex extension and re-evaluate fundamental principles of
time-frequency analysis. We provide a multicomponent model of a signal that
enables rigorous definition of instantaneous frequency on a per-component
basis. Within our framework, we have shifted all uncertainty of the latent
signal to its quadrature. In this approach, uncertainty is not a fundamental
limitation of analysis, but rather a manifestation of the limited view of the
observer. With the appropriate assumptions made on the signal model, the
instantaneous amplitude and instantaneous frequency can be obtained exactly,
hence exact representation of a signal in the coordinates of time and frequency
can be achieved. However, uncertainty now arises in obtaining the correct
assumptions, i.e.~how to correctly choose the quadrature of the components.
