time-domain-signal-generator.hpp

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

#include "abstract-signal-generator.hpp"

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

    /**
     * Generate a random (thanks to noise) one-dimensional signal in the time domain.
     *
     * Let the angular frequency be:
     * @code
     *      (omega) w = 2 * M_PI * frequency
     * @endcode
     * Where:
     *  - @code M_PI@endcode is the mathematical constant pi.
     *  - @code frequency@endcode is the frequency of the signal in seconds.
     *    It is the number of cycles that occur in one second (measured in Hertz, Hz).
     *  - @code 2 * M_PI@endcode is one complete cycle of a sine wave (in our case), which is 2*pi radians
     *    (note: a circle representing one complete oscillation has 2*pi radians).
     *  - @code 2 * M_PI@endcode is multiplied by @code frequency@endcode to get the angular frequency.
     *    So to find out how many radians are covered per second, we use this multiplication.
     *    In other words, it converts the frequency from cycles per second (Hz)
     *    to angular frequency in radians per second.
     *
     * The real part of the signal is generated using the cosine function:
     * @code
     *      cos(omega * time + phase) + noise
     * @endcode
     * Where time is the discrete time step at iteration i.
     *
     * Similarly, the imaginary part is generated using the sine function:
     * @code
     *      sin(omega * time + phase) + noise
     * @endcode
     *
     * A random noise is added to each formula to distort the signal.
     *
     * @param length The length of the signal. It represents the duration of the signal in discrete time steps.
     * @param frequency The frequency (Hz) of the signal.
     *                  In other words, it determines how many cycles (oscillations) the signal makes per second.
     * @param phase The phase (radians) of the signal.
     *              It represents the initial angle of the sine or cosine function at time t = 0.
     * @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 //TIME_DOMAIN_SIGNAL_GENERATOR_HPP