According to the Nyquist’s sampling theorem, aliasing will not occur provided the sampling rate is greater than twice the signal bandwidth. However, perfectly bandlimited signals do not occur in nature. Hence, some aliasing will still be present. To overcome this problem, an anti-aliasing filter is normally used to band-limit the incoming signal.

a)  Assume that a filtered signal has a spectrum which can be described by a 6th-order Butterworth filter, and upper cutoff frequency fc = 1000 Hz. obtain the expression for its power spectrum.

b)  Determine the sampling rate required so that aliasing is reduced to the -50 dB point in the power spectrum.

c) Repeat b) for a 12th-order Butterworth filter.