space-domain-signal-generator.hpp

#ifndef SPACE_DOMAIN_SIGNAL_GENERATOR_HPP
#define SPACE_DOMAIN_SIGNAL_GENERATOR_HPP
#include <complex>
#include <random>

#include "abstract-signal-generator.hpp"

class SpaceDomainSignalGenerator final : public AbstractSignalGenerator {
public:
    explicit SpaceDomainSignalGenerator(const std::optional<int> seed = std::nullopt) : AbstractSignalGenerator(seed) {}

    /**
     * Generate a random (thanks to noise) one-dimensional signal in the space domain.
     *
     * Let the spatial frequency be k = frequency.
     *
     * Let the unique spatial coordinate be x (since it's 1D).
     *
     * Let the phase shift be phi.
     *
     * The signal is generated using the formula:
     * @code
     *      signal(x) = (cos(2 * M_PI * k * x + phi) + noise) + j * (sin(2 * M_PI * k * x + phi) + noise)
     * @endcode
     * Where j is the imaginary unit.
     *
     * Using the parameters name of the function, the formula becomes:
     * @code
     *      signal(x) = (cos(2 * M_PI * frequency * x + phase) + noise) + j * (sin(2 * M_PI * frequency * x + phase) + noise)
     * @endcode
     *
     * In the mathematical literature, the formula is often written with its well-known form (Euler's formula):
     * @code
     *      signal(x) = exp(j * (2 * M_PI * k * x + phi))
     * @endcode
     *
     * A random noise is added to each formula to distort the signal.
     *
     * @param length The length of the signal. Specifies the number of points in the space domain.
     * @param frequency Represents the spatial frequency, which determines how many cycles occur per unit distance.
     *                  By "unit distance" we mean the distance between two consecutive samples in the spatial grid.
     *                  It can be meters, millimeters, or any other spatial unit.
     * @param phase The phase (shift) of the signal, which moves the waveform along the space axis (x since it's 1D).
     * @param noise The range of the random noise added to each sample of the signal.
     * @return The generated signal.
     */
    std::vector<std::complex<double>> generate1DSignal(int length, double frequency, double phase, double noise) override;
};

#endif //SPACE_DOMAIN_SIGNAL_GENERATOR_HPP