Getting Started

Requirements

• A C++17 compiler
• CMake 3.14 or newer if consuming via CMake.

constfilt is header-only. consteig and gcem are vendored under include/constfilt/vendor/ and are pulled in automatically by constfilt's own headers; no separate installation is needed.

Consuming the library

add_subdirectory

add_subdirectory(third_party/constfilt)
target_link_libraries(your_target PRIVATE constfilt::constfilt)

FetchContent

include(FetchContent)
FetchContent_Declare(
    constfilt
    GIT_REPOSITORY https://github.com/MitchellThompkins/constfilt
    GIT_TAG        main
)
FetchContent_MakeAvailable(constfilt)

target_link_libraries(your_target PRIVATE constfilt::constfilt)

constfilt::constfilt is an INTERFACE target that propagates the include path and the consteig / gcem dependencies transitively.

Header-only, no CMake

Add the constfilt, consteig, and gcem include directories to your compiler's include path, then #include <constfilt/constfilt.hpp>.

Hello, filter

#include <constfilt/constfilt.hpp>

int main()
{
    // 4th-order Butterworth lowpass, 100 Hz cutoff at 1 kHz sample rate.
    // All coefficient math happens at compile time.
    static constexpr constfilt::Butterworth<double, 4> bw(100.0, 1000.0);

    // Batch filtering.
    double input[8]{1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
    double output[8]{};
    bw(input, output);

    // Real-time sample-by-sample filtering (mutates internal state).
    constfilt::Butterworth<double, 4> rt(100.0, 1000.0);
    double y = rt(0.5);
}

Supported filters

• Butterworth: lowpass, highpass
• Elliptic: lowpass, highpass

All filter types support four discretization methods: TustinPW (prewarped bilinear, default), TustinNW (standard bilinear), ZOH, and MatchedZ.

The library imposes no upper bound on the filter order. The practical upper bound is set by double precision: as N grows, the magnitudes of polynomial coefficients and pole separations stretch over many orders of magnitude and round-off begins to dominate. The committed regression tests cover orders 1 through 8 because that is the range that is comfortably verifiable against Octave's reference implementations.

Selecting variants

// Lowpass / highpass (template parameter 4):
constfilt::Butterworth<double, 4> lp(100.0, 1000.0);
constfilt::Butterworth<double, 4, constfilt::TustinPW, constfilt::HighPass> hp(100.0, 1000.0);

// Discretization method (template parameter 3):
constfilt::Butterworth<double, 4, constfilt::TustinPW> tupw(100.0, 1000.0);  // default
constfilt::Butterworth<double, 4, constfilt::TustinNW> tunw(100.0, 1000.0);
constfilt::Butterworth<double, 4, constfilt::ZOH> zoh(100.0, 1000.0);
constfilt::Butterworth<double, 4, constfilt::MatchedZ> mz(100.0, 1000.0);

// Elliptic takes (cutoff_hz, passband_ripple_dB, stopband_atten_dB, sample_rate_hz):
constfilt::Elliptic<double, 4> el(100.0, 0.5, 60.0, 1000.0);
constfilt::Elliptic<double, 4, constfilt::TustinNW, constfilt::HighPass> el_hp(100.0, 0.5, 60.0, 1000.0);

// AnalogFilter defaults to TustinNW; TustinPW requires an explicit warp frequency:
constfilt::AnalogFilter<double, 2> af(b, a, 1000.0);
constfilt::AnalogFilter<double, 2, constfilt::TustinPW> af_pw(b, a, 1000.0,
                                                               constfilt::prewarp(100.0));

// Convenience aliases for first-order RC equivalents:
constfilt::FirstOrderLowPass<double> first_lp(100.0, 1000.0);
constfilt::FirstOrderHighPass<double> first_hp(100.0, 1000.0);

Accessing coefficients

The discretized transfer function is exposed as coeffs_b() and coeffs_a() on the underlying Filter, both constexpr:

static constexpr auto bw = constfilt::Butterworth<double, 2>(100.0, 1000.0);
// coeffs_b() and coeffs_a() return const T* that can be indexed:
constexpr double b0 = bw.coeffs_b()[0];
constexpr double a1 = bw.coeffs_a()[1];

Stability checking

AnalogFilter (the base of Butterworth and Elliptic) exposes a CheckStab template parameter (fourth parameter, default true) for stability checking (not yet implemented). To skip the check, pass CheckStab = false.