I have an
InterpolatingFunction constructed from a discrete set of values obtained by numerical methods. Let's denote it $f(x)$. The function demonstrates an oscillating behavior, with its amplitude and frequency gradually decaying. Here is an initial fragment of its graph; it continues to the right in the same manner:
I want to obtain two smooth monotone decreasing numerical functions $A(x),\omega(x)$ that approximate the decay rate of the amplitude and frequency, so that $f(x)\approx A(x) \cdot \sin\left(x\cdot\omega\!\left(x\right)\right)$. How can I approach this problem?