Firwin

[SpookyYomo]

This PR aims to implement Firwin.

Blockers before merging:

• Decision on Err implementation in Library ( Initial landing of Core #74 )
• Special Functions
• Arg Struct pattern
• Documentation fixes #61

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Original Message:

Currently opening as a draft PR to have eyes on the code before it grows even larger into eventually implementing firwin.

Questions I guess I need answers about specific to this repository to ensure the PR is decent:

1. What exactly in a function is allocating/otherwise for me to determine if the function name should be *_st or *_dyn?
2. File structure... As a first time contributor, it feels like it's just having many files and then being flattened by mod.rs to follow the scipy's submodule convention.... Individual files otherwise don't really make sense, and finding a function is best done either via grepping or through the [Source] button as created by cargo docs.
3. Doc's index.html: Maybe we should structure the Doc abit more clearly similar to Scipy's documentation where there's a clear header of Convolution, B-splines, Fitting, ...? I think this is achieveable with //!? Or I might be mistaken.
4. Unsafe code: I noticed some other functions using unsafe { F::from(-1).unwrap_unchecked) } or something similar. Is this the norm for "constants" which we can guarantee to be safe, and so I too should be doing this?

I will continue to force-push onto this branch with any suggestions such that each commit is consistent with its commit title and message.

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Note

Implements FIR filter design via firwin_dyn with validation and scaling, adds comprehensive window functions and Kaiser utilities, introduces an Error type, and updates signal module exports/docs.

• Filter design (signal/filter/design):
  • firwin_dyn: FIR filter design with argument validation, window application (custom or width-based Kaiser), scaling, and extensive tests.
  • Kaiser utilities: add kaiser_beta, kaiser_atten, kaiserord with tests.
• Windows (signal/windows):
  • Add GetWindow trait, Window enum, and get_window builder.
  • Implement windows: Boxcar, Triangle, Blackman, Hamming, Nuttall, Kaiser, GeneralCosine, GeneralGaussian, GeneralHamming (each with tests and docs).
• Errors:
  • New error::Error enum (InvalidArg, ConflictArg); export via lib.rs.
• Module/docs updates:
  • Expose signal::windows and enhance docs; integrate new design modules in signal::filter::design and adjust filter/wave docs.

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[SpookyYomo]

a92506d I have added error types after looking through how the Rust ecosystem generally does errors. This might still not be ideal and needs more work.

We should leave panics instead to Python-facing side of the library.

[SpookyYomo]

4598cbd There's still some redundancy in argument specification of Firwin. But I'm not sure how to resolve it.

Nonetheless it behaves to expectation now.

[SpookyYomo]

Forced push with rebase since Bessel trait has been merged.

[SpookyYomo]

Forced push with rebase since main has since bumped.
Also removed special-fun dependency since it was not removed in the last rebase.

[SpookyYomo]

Variadic arguments

There is https://crates.io/crates/variadics to resolve the struct-as-arg conundrum if we wish for a more pythonic interface, but I still believe that we should only keep the pythonic interface at the python binding level.
Related PR: #85

Design of interfaces

https://purplesyringa.moe/blog/the-expression-problem-and-rust/
The author argues on operational domains and data type as returns.
The reality is that rust intentionally does not intend to have implicit, hidden information
at a callsite, so an arg-struct pattern makes things more explicit.

[SpookyYomo]

An alternative is as done exactly in here,
but it also suffers the issue of variadic function lengths.

edit: The linked crate is almost certainly entirely AI generated, but it does show how
we could build ourselves into a corner.
edit 2: someone else points out an identical issue the exact same problem which Arg-Struct solves

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