7. Determine the z-transform of the following signals and sketch the pole-zero plot and ROC for each signal: a. x,[n] = ()"u[n + 2] + 3"u[=n – 1]

8

Q.4) Find the Legendre transform G(v1, v2, w) of the function F(u, из, w) — 2и{ — Зииз + из + Зwи,, where w is a passive variable. Justify that ƏF OG Jw Solution:-

Let A 1 E 1 = 2 — 0 3 Compute: (ATA)²

A.) Use a change of variables to generate expressions for 6 (t-t) and 6(w-wo) B. ) Use the expressions you just derived to show that & (t-t)=6(t-t) and S(w-wo)=6(wo-w) C.) Using your integral representations for 6, show that the following are Fourier pairs e^jwot2pi8(w-wo) 2pi6(t-to)e^jwT