Question

Can you please answer in simple steps:

e to Question 2. (2a) Show that a filter with the frequency response 2 x (104) HW) = w2 + 108 is physcially unrealizable. 2a Hint. Use the basic Fourier transform e-altl # for a > 0 and then the a2 +w2 time shifting property to obtain the inverse Fourier transform h(t) of H(w). Show that h(t) is noncausal. (2b) Can this filter be made approximately realizable by choosing a sufficiently large to? Use your own (reasonable) criterion of approximate realizability to determine to. Hint. Choose to so the exponential decays to 1% of the peak value.

Answer 1

01 HIW) 2x10 4 & swto. W 2+108 challl & FT Da Cota 2 2x104 W²+(10492 e 10h161 e swot alt) 4 3 Xlwtwol aftbol & Jwtax(s) [timescaling] we howe & 2x104 W24108 juto - 10"(t-fo] hlt) e-104ft-tol For causal system, the funch must not exist on the left side of the few axis. But graph of always exist in both sides of je axis. = hilts is a non causal system and practically unreali zable. e-161 the b ) e-sto. from HIWS we can obtain HLs)- MIS) 9x104 108-82 2x104 (10'+8)(104) HIS). - 10"ts lots taking inverse laplace fram form ㅗ TO'S edhe +

hie? - L"[hioJa (elo"? L'[HD] - tort.ult) toult-fo) u l-(& to)) te 6-1041f-do) ult-fol e 10h It-tol - same as by tourien. - This stolen is stable, the impulse response decays for Hloo so we can approximate the acbucal impulse response by sufficiently shitting to the right or by taking some large to and truncating ири - causal part.