lasp/cpp_src/dsp/lasp_avpowerspectra.h

#pragma once
#include "lasp_fft.h"
#include "lasp_mathtypes.h"
#include "lasp_timebuffer.h"
#include "lasp_window.h"

/** \defgroup dsp Digital Signal Processing utilities
 * These are classes and functions used for processing raw signal data, to
 * obtain statistics.
 *
 *
 * @{
 */

/**
 * @brief Computes single-sided cross-power spectra for a group of channels.
 * Only a single block of length fft, no averaging. This class should normally
 * not be used. Please refer to AvPowerSpectra instead.
 */
class PowerSpectra {
public:
  /**
   * @brief The FFT length
   */
  us nfft;

private:
  /**
   * @brief Instance to compute actual FFT's
   */
  Fft _fft;

  vd _window;
  d _scale_fac;

public:
  /**
   * @brief Initalize power spectra computer
   *
   * @param nfft The fft length
   * @param w The window type
   */
  PowerSpectra(const us nfft, const Window::WindowType w);

  /**
   * @brief Initalize power spectra computer
   *
   * @param window Uses the window length to compute fft length, and uses the
   * window shape as the actual window.
   */
  PowerSpectra(const vd &window);

  /**
   * @brief Computes the spectra. Data is normalized by the (spectral) power of
   * the window, to compensate for the effect of the window.
   *
   * @param input Input data, first axis is assumed the sample, second axis the
   * channel. Input first dimension should be equal to nfft, otherwise a
   * runtime error is thrown.
   *
   * @return Cross-power-spectra. Cubic array with size indices C_fij, where
   * f is the frequency index, i is the row and j is the column. An element
   * can be accessed by: C(f, i, j). Storage is such that frequency components
   * are contiguous.
   */
  ccube compute(const dmat &input);
};

/**
 * @brief Estimate cross-power spectra using Welch' method of spectral
 * estimation. The exact amount of overlap in Welch' method is rounded up to a
 * certain amount of samples.
 */
class AvPowerSpectra {

  enum class Mode {
    Averaging = 0,  // Averaging all time date
    Leaking = 1,    // Exponential weighting of an "instantaneous cps"
    Spectrogram = 2 // Instantenous spectrum, no averaging
  };

  Mode _mode;
  d _alpha;          // Only valid in case of 'Leaking'
  us _n_averages = 0; // Only valid in case of 'Averaging'

  PowerSpectra _ps;
  /**
   * @brief Current estimate of cross-spectral density
   */
  ccube _est;

  /**
   * @brief Buffer of storage of time data.
   */
  TimeBuffer _timeBuf;
  /**
   * @brief The amount of samples to keep in the overlap
   */
  us _overlap_keep;

public:
  /**
   * @brief Initalize averaged power spectra computer. If a time constant is
   * given > 0, it is used in a kind of exponential weighting.
   *
   * @param nfft The fft length
   * @param w The window type.
   * @param overlap_percentage A number 0 < overlap_percentage <= 100. It
   * determines the amount of overlap used in Welch' method. A typical value is
   * 50 %, i.e. 50.
   * @param fs_tau Value should either be < 0, indicating that the
   * estimate is averages over all time data.
   * For a value = 0 the instantaneous power spectrum is returned, which can be
   * interpreted as the spectrogram. For a value > 0 a exponential forgetting is
   * used, where the value is used as the time constant such that the decay
   * follows approximately the trend exp(-n/fs_tau), where n is the
   * sample number in the power spectra. To choose 'fast' time weighting, set
   * time_constant to the value of fs*0.125, where fs denotes the sampling
   * frequency.
   **/
  AvPowerSpectra(const us nfft = 2048,
                 const Window::WindowType w = Window::WindowType::Hann,
                 const d overlap_percentage = 50.,
                 const d fs_tau = -1);

  AvPowerSpectra(const AvPowerSpectra &) = delete;
  AvPowerSpectra &operator=(const AvPowerSpectra &) = delete;

  /**
   * @brief Reset to empty state. Clears the time buffer and sets estimator to
   * empty.
   */
  void reset();

  /**
   * @brief Compute an update of the power spectra based on given time data.
   * Note that the number of channels is determined from the first time this
   * function is called. If a later call has an incompatible number of
   * channels, a runtime error is thrown.
   *
   * @param timedata
   *
   * @return a copy of the latest estimate of the power spectra. an
   * update is only given if the amount of new time data is enough to compute a
   * new estimate. if no new estimate is available, it returns an empty ccube.
   * Note that the latest available estimate can be obtained using get_est().
   * */
  ccube compute(const dmat &timedata);

  /**
   * @brief Returns the latest estimate of cps (cross-power spectra.
   *
   * @return a copy of the latest estimate of the power spectra. an
   * update is only given if the amount of new time data is enough to compute a
   * new estimate. If no estimate is available, it returns an empty ccube.
   * */
  ccube get_est() const;

  /**
   * @brief The overlap is rounded to a certain amount of time samples. This
   * function returns that value.
   *
   * @return The amount of samples in overlapping.
   */
  us exactOverlapSamples() const { return _ps.nfft - _overlap_keep; }
};
/** @} */


/**
 * @brief Estimate cross-power spectra using Welch' method of spectral
 * estimation. The exact amount of overlap in Welch' method is rounded up to a
 * certain amount of samples. This class is specifically for sweeps and will ignore
 * fft blocks where the auto-power of the "reference" signal is below the average 
 * when in averaging mode.
 */
class AvSweepPowerSpectra {

  enum class Mode {
    Averaging = 0,  // Averaging all time date
    Leaking = 1,    // Exponential weighting of an "instantaneous cps"
    Spectrogram = 2 // Instantenous spectrum, no averaging
  };

  Mode _mode;
  d _alpha;          // Only valid in case of 'Leaking'
  us _nfft;
  vd _n_averages { 1, arma::fill::zeros}; // Only valid in case of 'Averaging'

  PowerSpectra _ps;
  /**
   * @brief Current estimate of cross-spectral density
   */
  ccube _est;

  /**
   * @brief Buffer of storage of time data.
   */
  TimeBuffer _timeBuf;
  /**
   * @brief The amount of samples to keep in the overlap
   */
  us _overlap_keep;

public:
  /**
   * @brief Initalize averaged power spectra computer. If a time constant is
   * given > 0, it is used in a kind of exponential weighting.
   *
   * @param nfft The fft length
   * @param w The window type.
   * @param overlap_percentage A number 0 < overlap_percentage <= 100. It
   * determines the amount of overlap used in Welch' method. A typical value is
   * 50 %, i.e. 50.
   * @param fs_tau Value should either be < 0, indicating that the
   * estimate is averages over all time data.
   * For a value = 0 the instantaneous power spectrum is returned, which can be
   * interpreted as the spectrogram. For a value > 0 a exponential forgetting is
   * used, where the value is used as the time constant such that the decay
   * follows approximately the trend exp(-n/fs_tau), where n is the
   * sample number in the power spectra. To choose 'fast' time weighting, set
   * time_constant to the value of fs*0.125, where fs denotes the sampling
   * frequency.
   **/
  AvSweepPowerSpectra(const us nfft = 2048,
                 const Window::WindowType w = Window::WindowType::Hann,
                 const d overlap_percentage = 50.,
                 const d fs_tau = -1);
                 
  AvSweepPowerSpectra(const AvSweepPowerSpectra &) = delete;
  AvSweepPowerSpectra &operator=(const AvSweepPowerSpectra &) = delete;

  /**
   * @brief Reset to empty state. Clears the time buffer and sets estimator to
   * empty.
   */
  void reset();

  /**
   * @brief Compute an update of the power spectra based on given time data.
   * Note that the number of channels is determined from the first time this
   * function is called. If a later call has an incompatible number of
   * channels, a runtime error is thrown.
   *
   * @param timedata
   *
   * @return a copy of the latest estimate of the power spectra. an
   * update is only given if the amount of new time data is enough to compute a
   * new estimate. if no new estimate is available, it returns an empty ccube.
   * Note that the latest available estimate can be obtained using get_est().
   * */
  ccube compute(const dmat &timedata);

  /**
   * @brief Returns the latest estimate of cps (cross-power spectra.
   *
   * @return a copy of the latest estimate of the power spectra. an
   * update is only given if the amount of new time data is enough to compute a
   * new estimate. If no estimate is available, it returns an empty ccube.
   * */
  ccube get_est() const;

  /**
   * @brief The overlap is rounded to a certain amount of time samples. This
   * function returns that value.
   *
   * @return The amount of samples in overlapping.
   */
  us exactOverlapSamples() const { return _ps.nfft - _overlap_keep; }
};
/** @} */