biquad.hpp

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/*
 * eDSP, A cross-platform Digital Signal Processing library written in modern C++.
 * Copyright (C) 2018 Mohammed Boujemaoui Boulaghmoudi, All rights reserved.
 *
 * This program is free software: you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the Free
 * Software Foundation, either version 3 of the License, or (at your option)
 * any later version.
 *
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of  MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
 * more details.
 *
 * You should have received a copy of the GNU General Public License along width
 * this program.  If not, see <http://www.gnu.org/licenses/>
 *
 * File: biquad.hpp
 * Date: 09/06/18
 * Author: Mohammed Boujemaoui
 */

#ifndef EDSP_FILTER_BIQUAD_HPP
#define EDSP_FILTER_BIQUAD_HPP

#include <edsp/math/numeric.hpp>
#include <edsp/meta/expects.hpp>
#include <algorithm>
#include <cmath>
#include <functional>
#include <complex>

namespace edsp { namespace filter {

    enum class FilterType {
        LowPass,           
        HighPass,          
        BandPassSkirtGain, 
        BandPassPeakGain,  
        BandPass,          
        BandStop,          
        AllPass,           
        LowShelf,          
        HighShelf,         
        BandShelf,         
        Notch,             
        PeakingEQ          
    };

    template <typename T>
    class biquad {
    public:
        using value_type = T;

        constexpr biquad() noexcept              = default;
        constexpr biquad(const biquad&) noexcept = default;
        constexpr biquad(biquad&&) noexcept      = default;
        constexpr biquad& operator=(const biquad&) noexcept = default;
        constexpr biquad& operator=(biquad&&) noexcept = default;

        constexpr biquad(const std::complex<T>& pole, const std::complex<T>& zero);

        constexpr biquad(const std::complex<T>& pole_first, const std::complex<T>& zero_first,
                         const std::complex<T>& pole_second, const std::complex<T>& zero_second);

        constexpr biquad(value_type a0, value_type a1, value_type a2, value_type b0, value_type b1,
                         value_type b2) noexcept;
        ~biquad() = default;

        constexpr value_type a0() const noexcept;

        constexpr value_type a1() const noexcept;

        constexpr value_type a2() const noexcept;

        constexpr value_type b0() const noexcept;

        constexpr value_type b1() const noexcept;

        constexpr value_type b2() const noexcept;

        constexpr void set_a0(T value) noexcept;
        constexpr void set_a1(T value) noexcept;

        constexpr void set_a2(T value) noexcept;

        constexpr void set_b0(T value) noexcept;

        constexpr void set_b1(T value) noexcept;

        constexpr void set_b2(T value) noexcept;

        template <typename InputIt, typename OutputIt>
        constexpr void filter(InputIt first, InputIt last, OutputIt d_first);

        constexpr void reset() noexcept;

        constexpr bool stability() const noexcept;

        constexpr explicit operator bool() const noexcept;

        constexpr value_type tick(T value) noexcept;

    private:
        value_type b2_{0};
        value_type b1_{0};
        value_type b0_{1};
        value_type a2_{0};
        value_type a1_{0};
        value_type a0_{1};
        value_type w0_{0};
        value_type w1_{0};
    };

    template <typename T>
    constexpr biquad<T>::biquad(value_type a0, value_type a1, value_type a2, value_type b0, value_type b1,
                                value_type b2) noexcept :
        b2_(b2 / a0),
        b1_(b1 / a0),
        b0_(b0 / a0),
        a2_(a2 / a0),
        a1_(a1 / a0),
        a0_(1) {}

    template <typename T>
    constexpr biquad<T>::biquad(const std::complex<T>& pole, const std::complex<T>& zero) :
        b2_(0),
        b1_(1),
        b0_(-zero.real()),
        a2_(0),
        a1_(-pole.real()),
        a0_(1) {
        meta::expects(pole.imag() == 0, "Expecting real pole");
        meta::expects(zero.imag() == 0, "Expecting real zero");
    }

    template <typename T>
    constexpr biquad<T>::biquad(const std::complex<T>& pole_first, const std::complex<T>& zero_first,
                                const std::complex<T>& pole_second, const std::complex<T>& zero_second) :
        b0_(1),
        a0_(1) {
        if (pole_first.imag() != 0) {
            meta::expects(pole_second == std::conj(pole_first), "Expecting complex conjugates");
            a1_ = -2 * pole_first.real();
            a2_ = std::norm(pole_first);
        } else {
            meta::expects(pole_second.imag() == 0, "Expecting a complex number");
            a1_ = -(pole_first.real() + pole_second.real());
            a2_ = pole_first.real() * pole_second.real();
        }

        if (zero_first.imag() != 0) {
            meta::expects(zero_second == std::conj(zero_first), "Expecting complex conjugates");
            b1_ = -2 * zero_first.real();
            b2_ = std::norm(zero_first);
        } else {
            meta::expects(zero_second.imag() == 0, "Expecting a complex number");
            b1_ = -(zero_first.real() + zero_second.real());
            b2_ = zero_first.real() * zero_second.real();
        }
    }

    template <typename T>
    constexpr void biquad<T>::reset() noexcept {
        w0_ = 0;
        w1_ = 0;
    }

    template <typename T>
    constexpr bool biquad<T>::stability() const noexcept {
        return std::abs(a2_) < 1 && (std::abs(a1_) < (1 + a2_));
    }

    template <typename T>
    constexpr void biquad<T>::set_a0(const value_type value) noexcept {
        a0_ = value;
        reset();
    }

    template <typename T>
    constexpr void biquad<T>::set_a1(const value_type value) noexcept {
        a1_ = value;
        reset();
    }

    template <typename T>
    constexpr void biquad<T>::set_a2(const value_type value) noexcept {
        a2_ = value;
        reset();
    }

    template <typename T>
    constexpr void biquad<T>::set_b0(const value_type value) noexcept {
        b0_ = value;
        reset();
    }

    template <typename T>
    constexpr void biquad<T>::set_b1(const value_type value) noexcept {
        b1_ = value;
        reset();
    }

    template <typename T>
    constexpr void biquad<T>::set_b2(const value_type value) noexcept {
        b2_ = value;
        reset();
    }

    template <typename T>
    template <typename InputIt, typename OutputIt>
    constexpr void biquad<T>::filter(InputIt first, InputIt last, OutputIt d_first) {
        for (; first != last; ++first, ++d_first) {
            *d_first = tick(*first);
        }
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::tick(const value_type value) noexcept {
        const auto out = b0_ * value + w0_;
        w0_            = b1_ * value - a1_ * out + w1_;
        w1_            = b2_ * value - a2_ * out;
        return out;
    }

    template <typename T>
    constexpr biquad<T>::operator bool() const noexcept {
        return stability();
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::a0() const noexcept {
        return a0_;
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::a1() const noexcept {
        return a1_;
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::a2() const noexcept {
        return a2_;
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::b0() const noexcept {
        return b0_;
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::b1() const noexcept {
        return b1_;
    }

    template <typename T>
    constexpr typename biquad<T>::value_type biquad<T>::b2() const noexcept {
        return b2_;
    }
}} // namespace edsp::filter

#endif // EDSP_FILTER_BIQUAD_HPP