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Generally I'd recommend it though. For linear algebra there's ndarray, nalgebra, faer, ... depending on what you need. I'm not familiar with the precise options for the other stuff you need but there are crates for kalmann filters etc. - your best bet is probably just searching crates.io with some keywords.
It's not terribly difficult to build a multidimensional FFT on top of it, although to your point first-class support would be nice
And in the rare case that Julia isn't enough, Julia-Rust interop is pretty good! Julia can call Rust using ccall and Rust can call Julia using the jlrs crate.