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Since your signal isn't sampled uniformly some strange things might happen when you apply FFT and look at the results. What you should do is estimate the Uniform DFT of the Non Uniform Time Series. One easy way to do it is use the reference code and analysis I posted on the question - Frequency Analysis of a Signal Without a Constant Sampling Frequency (...

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My guess would be that the DC peak is part of the transient response, thus it decreases to zero over time T as the oscillating parts of your signal continue. But I don't know what your signal is so that's a guess

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The DFT Matrix for Non Uniform Time Samples Series Problem Statement We have a signal $x \left( t \right)$ defined on the interval $\left[ {T}_{1}, {T}_{2} \right]$. Assume we have $N$ samples of it given by $\left\{ x \left( {t}_{i} \right) \right\}_{i = 0}^{N - 1}$. The samples time ${t}_{i}$ is arbitrary and not necessarily uniform. We're ...

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