Hyperbolic antilogarithms are simple exponentials, i.e.
If the quadratic (38) has a negative root, the trigonometrical functions in (36) are to be replaced by real exponentials, and the position x=o, y=o is unstable.
For damped exponentials, the ordering is by energy spectral density at the peak frequency.
This method shed some new light on the estimation of complex exponentials in white noise.
Instead of a simple exponential, the process is made up of lots of exponentials!
The primary utility of this procedure rests in fitting damped sines or the damped exponentials that occur in multicomponent exponential decays.
undamped sines, and damped exponentials.
Using this method, it is possible to fit exponentially damped sines, undamped sines, and damped exponentials.
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