hilbert.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: hartley.hpp
 * Author: Mohammed Boujemaoui
 * Date: 3/8/2018
 */
#ifndef EDSP_HILBERT_HPP
#define EDSP_HILBERT_HPP

#include <edsp/spectral/internal/fft_impl.hpp>
#include <edsp/converter/real2complex.hpp>
#include <edsp/math/numeric.hpp>
#include <vector>

namespace edsp { inline namespace spectral {

    template <typename InputIt, typename OutputIt,
              typename Allocator = std::allocator<std::complex<meta::value_type_t<InputIt>>>>
    inline void hilbert(InputIt first, InputIt last, OutputIt d_first) {
        using value_type = meta::value_type_t<InputIt>;
        const auto nfft  = static_cast<typename fft_impl<value_type>::size_type>(std::distance(first, last));

        std::vector<std::complex<value_type>, Allocator> input_data(nfft);
        std::vector<std::complex<value_type>, Allocator> complex_data(nfft);
        edsp::real2complex(first, last, std::begin(input_data));

        fft_impl<value_type> fft(nfft);
        fft.dft(meta::data(input_data), meta::data(complex_data));

        const auto limit_1 = math::is_even(nfft) ? nfft / 2 : (nfft + 1) / 2;
        const auto limit_2 = math::is_even(nfft) ? limit_1 + 1 : limit_1;
        for (auto i = 1; i < limit_1; ++i) {
            complex_data[i] *= 2;
        }

        for (auto i = limit_2; i < nfft; ++i) {
            complex_data[i] = std::complex<value_type>(0, 0);
        }

        fft_impl<value_type> ifft(nfft);
        ifft.idft(meta::data(complex_data), &(*d_first));
        ifft.idft_scale(&(*d_first));
    }

}} // namespace edsp::spectral

#endif // EDSP_HIRTLEY_HPP