Question

V Q11) Consider an xa (t) with BW (max. frequency) W in Hz. The sampling rate is chosen to be above the Nyquist rate at F (1/T ) 3W. xa (t) is reconstructed according to the formula below, where WIW2. Determine the respective values of W1 and W2, both in terms of W, so that the formula below reconstruction yields perfect Xa (nT)h(t-nT) n=-oo Where sin (2tW1t) sin (2tW2t) 1 Ts 2W1 h(t) Tit Tt and 3W 3W .LLLLOLI

Answer 1

Yalf) Fs = 3W. na(t)= Z nal Ts h(t-nTs nalt) na(nTs) St Ts (2n W, t) Sn (2nwt) htt) = Sm 2W, TTt Sin (at) 9tect 20 Sen (2nk/t) 91ect 2(2nW) TTL 2nw 2nW -2nw2 2nW2 CWe know (t) n2lt) 277 The convolutien e above too nect 's coll gve

olP d Convolutren 210 -2ntoyta 2n/0) Ts NOo, 20, Te 20, Sampled Spectur Fmal Olp Ts -2nlog 2n0A Now h Coe coant penfect vecong tauctien then c250 W co2-0 7 0.5. Dto 3,5 MET Co-1.50