add formula description to EA

R/excess_attenuation.R

@@ -11,7 +11,7 @@
 #' @return Object 'X' with an additional column,  'excess.attenuation', containing the computed excess attenuation values (in dB).
 #' @export
 #' @name excess_attenuation
-#' @details Excess attenuation is the amplitude loss of a sound in excess due to spherical spreading (observed attenuation - expected attenuation). With every doubling of distance, sounds attenuate with a 6 dB loss of amplitude (Morton, 1975; Marten & Marler, 1977). Any additional loss of amplitude results in energy loss in excess of that expected to occur with distance via spherical spreading. So it represents power loss due to additional factors like vegetation or atmospheric conditions (Wiley & Richards, 1978). Low values indicate little additional attenuation. The goal of the function is to measure the excess attenuation on sounds in which a reference playback has been re-recorded at increasing distances. The 'sound.id' column must be used to indicate which sounds belonging to the same category (e.g. song-types). The function will then compare each sound type to the corresponding reference sound. Two approaches for computing excess attenuation are provided (see 'type' argument). NAs will be returned if one of the envelopes is completely flat (e.g. no variation in amplitude).
+#' @details Excess attenuation is the amplitude loss of a sound in excess due to spherical spreading (observed attenuation - expected attenuation). With every doubling of distance, sounds attenuate with a 6 dB loss of amplitude (Morton, 1975; Marten & Marler, 1977). Any additional loss of amplitude results in energy loss in excess of that expected to occur with distance via spherical spreading. So it represents power loss due to additional factors like vegetation or atmospheric conditions (Wiley & Richards, 1978). Excess attenuation is computed as \code{-20 * log10(rms("test signal") / rms("reference signal"))) - (20 * log10(1 / "distance")} in which 'rms(..)' represents the root mean squared of an amplitude envelope. Low values indicate little additional attenuation. The goal of the function is to measure the excess attenuation on sounds in which a reference playback has been re-recorded at increasing distances. The 'sound.id' column must be used to indicate which sounds belonging to the same category (e.g. song-types). The function will then compare each sound type to the corresponding reference sound. Two approaches for computing excess attenuation are provided (see 'type' argument). NAs will be returned if one of the envelopes is completely flat (e.g. no variation in amplitude).
 #' @examples {
 #'   # load example data
 #'   data("test_sounds_est")