# How does Mathematica's LowpassFilter work?

I don't really understand the documentation for the LowpassFilter[] function in Mathematica. In the course I have about signal processing, low-pass filters come in many different forms and from different kinds of operations, so I was just wondering if someone could explain to me the math behind this specific function.

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Putting this together, we can see that the default values for LowpassFilter calculate the $n$th order linear FIR filter that is closest to the specified frequency response (in a mean-squares sense), assuming preprocessing by a Hamming window.
Thanks! $\phantom{}$ –  L1meta Jun 7 at 19:34