EG7016 - Why is an Anti-Aliasing Filter Needed - Engineering Assignment Help

Assignment Task

Question 2
The electroencephalogram (EEG) is the record of the electrical activity of the brain and it has harmonics of interest up to 100 Hz. The EEG of a patient was filtered using an analogue antialiasing filter. From that filtered version of the EEG, a discrete signal was constructed with a sequence of 8192 equally spaced samples x(n), with T=4 ms and n=0, 1, …, 8191. A DFT was then performed on the discrete time sequence to produce a 8192-point sequence X(k).
(a) Why is an anti-aliasing filter needed?
(b) What type of filter is the anti-aliasing filter (low-pass, high-pass, band-pass or band-reject)?
(c) Is the sampling period T=4 ms, adequate? Explain.
(d) Would the result be different if an FFT was applied rather than a DFT? Why? Why not?
(e) The alpha waves of the EEG are in the range 8 Hz-15 Hz and are useful to determine if a patient is in a coma. Which coefficients k, of X(k) would correspond to the alpha waves of the EEG?
(f) What parameters would need to be changed, and how, to increase the frequency resolution of this FFT, which is being used as a ‘spectrum analyser’?
(g) If a DFT of 8192 points takes 10 ms to be executed on a certain computer, how long would a DFT of 4096 points take on the same computer? Explain.

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