An octave is defined as a doubling of the frequency. The claim is made that a low-pass Butterworth filter of order n has a roll-off (attenuation) of 6n dB/octave. Calculate the gain in dB for a second-order filter for the cut-off frequency itself, and for three octaves above the cut-off frequency, i.e., for f/f cut off = 1, 2, 4, and 8. Then determine the roll-off in dB per octave. Does the calculated roll-off agree with the stated value of 6n dB/octave? Is the agreement better for low frequencies or high frequencies? Repeat for filters of order 4 and 6.