A complex demodulation technique based on the Hilbert transform is applied to hot‐film velocity measurements of the flow over a rotating disk. As the cross‐flow instability of the boundary layer of the disk sets in, finite bandwidth packets of Fourier modes appear and grow along the radius. These wave packets, giving strong amplitude and frequency modulations, allow the calculation of the envelope and instantaneous frequency of the signals. This decomposition in amplitude and frequency is used to determine different behaviors of the flow as the Reynolds number increases. Three concentric regions are accurately detected: a first one consisting of a linear growth of disturbances, a second zone where the flow becomes more organized, and finally a turbulent region. The transition to turbulence is also precisely determined and allows an interpretation in terms of defects (amplitude holes) occurring in the flow pattern.