This problem provides another derivation of the structure for the coupled-form oscillator by considering the system y(n) = ay(n – 1) + x(n), for a = ejω0. Let x(n) be real. Then y(n) is complex. Thus, y(n) = yR(n) + jyl(n)
(a) Determine the equations describing a system with one input x(n) and the two outputs yR(n) and yl(n).
(b) Determine a block diagram realization
(c) Show that if x(n) = ∂(n), then yR (n) = (cos ω0n)u(n), yl(n) = (sin ω0n)u(n)
(d) Compute yR(n), yl(n). n = 0, 1. . . 9 for ω0 = π/6. Compare these with the true values of the sine and cosine