1. A digital power vacuum tube amplifier emulator comprising: a system input; a feedback signal; an input sample resulting from subtracting the said feedback signal from said system input; an output sample; a digital sample processor; a first comparison function to determine if the said input sample is greater or less than a first threshold value; a second comparison function to determine if the said input sample is greater or less than a second threshold value; a negative clipping function to produce a negative clipping sample by dividing a first numerator sample by a first denominator sample, the said first numerator sample produced by adding the said input sample to a first coefficient, and the said first denominator sample produced by subtracting the said input sample from a second coefficient; a positive clipping function to produce a positive clipping sample by dividing a second numerator sample by a second denominator sample, the said second numerator sample produced by adding the said input sample to a third coefficient, and the said second denominator sample produced by adding the said input sample to a fourth coefficient; a linear function to produce a linear sample by multiplying the said input sample by a gain coefficient; an output sample selector to select the said output sample, the said output sample selector selecting the said negative clipping sample when the said input sample is less than the said first threshold value, the said output sample selector selecting the said positive clipping sample when the said input sample is greater than the said second threshold value, and the said output sample selector selecting the said linear sample when the said input sample is both greater than the said first threshold value and less than the said second threshold value; a system output resulting from the said output sample; a feedback network comprising a linear filter, producing said feedback signal by filtering said system output; an implicit numerical integration solver function to compute said system output from said system input.