pm-remez: Parks-McClellan Remez FIR design algorithm

pm-remez is a modern Rust implementation of the Parks-McClellan Remez exchange algorithm. It can be used as a Rust library and as a Python package via its Python bindings.

pm-remez supports the design of FIR filters with even symmetry and odd symmetry, and with an even number of taps and an odd number of taps, by reducing all these cases to the even symmetry odd number of taps case. The desired frequency response in each band, as well as the weights, can be defined as arbitrary functions. The library can use double-precision IEEE 754 floating-point numbers for calculations, as well as other higher precision floating-point implementations, such as num-bigfloat. This can be used to solve numerically challenging problems that are difficult to solve using double-precision arithmetic.

The implementation draws ideas from a paper by S.I. Filip to make the algorithm robust against numerical errors. These ideas include the use of Chebyshev proxy root finding to find the extrema of the weighted error function in the Remez exchange step.

Documentation

The documentation for the Rust crate is hosted in docs.rs/pm-remez.

The documentation for the Python package is hosted in pm-remez.readthedocs.io.

The Python package documentation contains a series of examples that show how to use pm-remez to design commonly used types of FIR filters. These illustrate the capabilities of pm-remez and also serve as a filter design guide. The documentation of the Rust crate contains a few examples of the Rust API. The Python examples can also be written in Rust (and in fact this is done as part of integration testing).

Python package

The pm-remez Python package is published in PyPI. There are pre-built binary packages for common architectures and operating systems. For these, the package can be installed by doing

pip install pm-remez

Building

The pm-remez crate uses ndarray-linalg to solve eigenvalue problems. This in turn depends on LAPACK. The pm-remez crate has several feature flags that are used to select the LAPACK backend. Exactly one of these features needs to be enabled to build pm-remez. The feature flags are openblas-static, openblas-system, netlib-static, netlib-system, intel-mkl-static and intel-mkl-system. The -static versions of each flag build the LAPACK backend and link statically against it. The -system versions link against a system-installed library (linking can be dynamic or static depending on which type of library is installed). For example,

cargo build --release --features openblas-system

will build against a system-installed OpenBLAS library.

The Python package is built using maturin. It can be built with

maturin build --release

or

python -mbuild

License

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.