Two finite-duration sequences h₁[n] and h₂[n] of length 8 are sketched in Figure. The two sequences are related by a circular shift, i.e., h₁[n] = h₂[((n ? m)) 8].

(a) Specify whether the magnitudes of the eight-point DFTs are equal.

(b) We wish to implement a lowpass Fir filter and must use either h₁[n] or h₂[n] as the impulse response. Which one of the following statements is correct?

(i) h₁[n] is a better lowpass filter than h₂[n].

(ii) h₂[n] is a better lowpass filter than h₁[n].

(iii) The two sequences are both about equally good (or bad) as lowpass filters.

Transcribed Image Text:

h;[n} 0 1 2 3 4 5 6 7 (a) 0 1 2 3 4 5 6 7 (b)