Question

Signal and system (I already have solution pls plot the function)

Question 2: Let Zi (t) = Σ00-oo akejinkt and let x2(t) = Σ00-00 bkejinkt. Here assume ak 〉 0 yk and that Compute and plot y(t) Solution: Here we have perio k, when |k| = 1 and bk - o otherwise. Further define y(t) - 17i(T)x2(t -T)dT d T = 1 and W-2T. Now y(t) = 11-1(T)22(t-T)dr bkw dr (Substituting for r2(t -T) T1 (T =ibeekut (1hzī(r)e-jk."dr) (Interchanging sum and integr = 〉 bkejku, tak | S ince ak -

Answer 1

It is Given that a_k > 0 Forall k & b_k = k/a_k when Vertical-bar k Vertical-bar = 1 or k = plusminus 1 & b_k = 0 when Vertical-bar k Vertical-bar notequalto 1 or k notequalto 1 so, b_- infinity to b_- 2 = 0 and b_0 = 0 and b_2 to b_infinity = 0 & b_1 = 1/a_1 & b_- 1 = -1/a_- 1 now, y (t) = sigma_k a_k b_k e^j w t = a_- infinity b_- infinity^0 e^i (- infinity) w t + . . . . . + b_- 2^0 a_- 2 e^i (- 2) w t + b_- 1 a_- 1 e^j (- 1) w t + b_0^0 + a_1 b_1 e^i (1) w t + a_2 b^0_2 e^j (2) w t + . . . . + a_infinity b^0_infinity e^i (infinity) w t = b_- 1 a_- 1 e^- j w t + a_1 b_1 e^j w t = -1/a_- 1 (a_- 1) e^