2.12. Aliasing will not occur if the sampling rate is greater than twice the signal band- width. However, perfectly bandlimited signals do not occur in nature. Hence, there is always some aliasing present. (a) Suppose that a filtered signal has a spectrum described by a Butterworth filter with order n = 6, and upper cutoff frequency f = 1000 Hz. What sampling rate is required so that aliasing is reduced to the -50 dB point in the power spectrum? (b) Repeat for a Butterworth filter with order n =12. There are several useful approximations to the ideal low-pass filter character- istic. One of these, the Butterworth filter, approximates the ideal low-pass filter with the function 1 |H,(f)| = n ≥ 1 √√1+ (f/fu)²n (1.65) where f is the upper -3-db cutoff frequency and n is referred to as the order of the filter.