Current multitaper implementation too slow for continuous raw data

Describe the new feature or enhancement

Currently, it is basically impossible to use raw.compute_psd(method="multitaper", bandwidth=1). For long data, it calculates hundreds of DPSS windows and therefore it takes way too long. In the example below, I used bandwidth=1 which is one of the fastest settings but it takes 6 minutes for a single raw array with shape (376 x 277s * 600Hz) (taken from this tutorial). I did not have time to test how long it takes for bandwidth=4 but probably more than 20 minutes on an M1 MacBook Pro.

Describe your proposed implementation

I am not very familiar with multitapers. However, it should be really easy to speed up the implementation, by simply calculating the multitapers on epochs of the raw data and averaging afterwards.

I discussed this at the CuttingMEEG conference with @britta-wstnr and I think she agreed.

Describe possible alternatives

Multitaper too slow: Jupyter Notebook

Additional context

No response

Start at the raw.compute_psd(method="multitaper", bandwidth=1) entry point and review the linked raw overview tutorial and multitaper_too_slow notebook for the reported workload. Compare the current continuous-data behavior with the proposed epoch-based calculation and averaging approach. Done means multitaper PSD for long raw data is substantially faster while preserving the expected result.