Thursday, March 8, 2007

Stationary Signals

1. General illustration
The first natural division of all signals is into either stationary or non-stationary categories. Stationary signals are constant in their statistical parameters over time. If you look at a stationary signal for a few moments and then wait an hour and look at it again, it would look essentially the same, i.e. its overall level would be about the same and its amplitude distribution and standard deviation would be about the same. Rotating machinery generally produces stationary vibration signals.
Stationary signals are further divided into deterministic and random signals. Random signals are unpredictable in their frequency content and their amplitude level, but they still have relatively uniform statistical characteristics over time. Examples of random signals are rain falling on a roof, jet engine noise, turbulence in pump flow patterns and cavitation. In fact, most random signals in nature could be treated as wide-sense stationary.
2. Mathematically
Reference to the picture from the article "The empirical mode decomposition and theHilbert spectrum for nonlinear andnon-stationary time series analysis" by Norden E. Huang et. al. Page 3

On Instantaneous Frequency

Instantaneous Frequency的定义是相位的导数,不是初相的,不可搞混