Assume we have a dataset containing 1000 floating-point numbers. Its power spectral density function (PSD) can be estimated using various methods, e.g. Welch's method.

Unlike above, please consider a dynamic dataset every time a new datum arrives into (its size increases like 1001, 1002, and so on). Conventionally, PSD can be computed every time by considering the entire dataset.

However, I wonder, if PSD can be updated without computing the entire dataset at a desired instance?

Such trick can be seen in the cumulative moving average; please see the 2nd equation therein.

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    $\begingroup$ You're looking for the Sliding (window) DFT. $\endgroup$ – Marcus Müller Jun 6 '18 at 12:39

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