IIR-Filters

A C++17 library implementing Infinite Impulse Response (IIR) digital filters.

This is primarily a personal learning experiment for understanding IIR digital filters. This project focuses on accuracy and compatibility with reference implementations from SciPy and Vinnie Falco's DSPFilters project. Correctness and readability are primary goals, while being the fastest implementation is not.

Aside from dependencies for tests and examples, this project uses only the C++ standard library. Dependencies are managed using CMake FetchContent.

Features

• Prototype filters: Butterworth, Chebyshev Type I/II, Elliptic, Bessel, and Legendre (Optimum-L)
• Frequency transformations: Lowpass, highpass, bandpass, and bandstop
• Filter representations: Zero-Pole-Gain (Zpk), second-order sections (SOS), and biquad cascades
• Mathematical utilities: Elliptic integrals, polynomial root finding, and complex number handling

Building

cmake -B build -DCMAKE_BUILD_TYPE=Release -G Ninja
cmake --build build

Run tests:

./build/test/tests

Build and run UI example:

cmake -B build -DCMAKE_BUILD_TYPE=Release -DBUILD_DEMO=ON
cmake --build build
./build/examples/imgui_demo/imgui_demo

Example Usage

#include "filters.hpp"

using namespace iirfilters;

// Design a 4th-order Butterworth lowpass filter at 1kHz (48kHz sample rate)
auto zpk = butterworthPrototype(4);
zpk = lowpassToLowpass(zpk, 1000.0, 48000.0);
auto sos = zpk.toSos();
Cascade filter(sos);

// Process samples
double output = filter.process(inputSample);

See also

The following codebases were essential resources in creating this library.

• DSPFilters
• Netlib Cephes - Elliptic integral implementations
• scipy.signal filter design - Primary reference and model for filter algorithms