I have a periodic time series data that are constantly sent to server from machines. It has uneven sampling rate.
I want to quantify measure of oscillations by combining information about frequency + amplitude of oscillations.
To my knowledge, Fourier transformation handles this, but it works only when the sampling rate is constant. Mine is not, which forced me to use Lomb-Scargle transformation to extract information about dominant frequency. Unfortunately, Lomb-Scargle periodogram does not preserve the amplitude of the original data.
I tried both FFT and Lomb-Scarlge. FFT completely failed, but Lomb-Scargle succeeded in capturing dominant frequencies, but still, did not preserve amplitude of the original data
So I want to scale my Lomb-scargle periodogram so that it contains information about the amplitude of the original data.
Consider the following time series:
I want to capture information about amplitude of oscillation, and how often that occurs with:
$$\frac{1}{N}\sum_{i=1}^N{\frac{\Delta y_i}{t_i}}=(\frac{\Delta y_1}{\Delta t_1} + \frac{\Delta y_2}{\Delta t_2} + \frac{\Delta y_3}{\Delta t_3} \, \cdots \, \frac{\Delta y_N}{\Delta t_N}) / (1 - N)$$
Is this a valid approach? I am concerned that the sampling rate is uneven, and it might affect my approach. And also the change in amplitude is affected by when it was recorded. For example, $\Delta y_2$ and $\Delta y_3$ are captures over the similar $\Delta t$, and yet the absolute difference in magnitude is largely different.
If my approach is not right, is there any other suggestions?