Question

4. Nyquist pulses. Let 9rx[n] be a (discrete-time) pulse shaping filter, Grx[n] be the causal) matched filter for 9rx[n], and p[n] be the convolution of grx[n] and gex (n). Suppose that p[n] is a Nyquist pulse. Finally, let there be P = 7 samples per symbol interval. Answer the following as "always true" or "possibly false," and give a brief reason. (a) p[0] = 0 (b) p[0] = 1 (c) p[7] = 0 (d) 9tx[0] = 1 (e) 9rx[7] = 1

Answer 1

Given data gegen. zibea (discrete-time) pulse shaping filter g (n) is a (causal bygnist pulse matched 14 filter, Pon) = 9, (n) Ⓡ 9 () P = 7 sample per symbol interval putse shaping ite u trecuency Orxan paswombly Pnx Onx com af1 nxo Tenco @ PO)=0 no __p00) = Jox!0) @ Inlos IŽ 9, 60-9 (0-K) 2009 I J (0) Brul-K) - 01). Omg l-E2 Ž. 1. Joe (+) -92-1) =D 3 Axo zo when K=1 Saxo zo no 8(0)=0 always true BPO) 21 110=o is always true plo = 1 is possibly false, © Plu) = 0 p14) - Ž 2,42) - Inç 13 =) DC when K7 then and only p( 720 is always true otherwise possibly talse

@ grt0) = 1 from a cm graph citats alwaye true. © 9.)=1 By shifting go grx (n) graph with "3 is always true