these functions are documented by mathworks and are well known in the art the example of fig1 operates to preserve the perceived spectral balance in the processed audio by employing in the compute gains per band 8 of fig1 non linear gain to loudness functions based on the human auditory system such as shown in fig1 the plot in fig1 shows that there is a substantially linear relationship between the logarithm of loudness and the logarithm of sound pressure level provided that the amplitude is above the linearity threshold below this linearity threshold loudness drops off more rapidly as the audio sound pressure level approaches and then falls below the threshold of hearing which is the point where the slope of the sound pressure level to loudness curve approaches vertical in order to modify the perceived loudness of an audio signal by a prescribed loudness ratio one may represent this as a prescribed shift up or down on the log loudness axis of fig1 for example if one wishes to halve the loudness of a 1 khz signal one may apply the process shown in fig1 the process operates as follows 1 measure the amplitude of the input signal for example rms amplitude in one frequency band for example a band of frequencies.