(1 point) Find y as a function of t if 16y" – 32y + 20y = 0, and y(1) = 9, y' (1) = 4. y =
4. Let h(t), (t), and y(t), for -oo < oo, be the impulse response function, the input, and the output of a linear time-invariant system, respectively. Give the following spectra: Input magnitude spectrum: Input phase spectrum: ex(2) T/2 Output magnitude spectrum: tY() Output phase spectrum: ey (2) / 2 Find H() from the above spectra and from the fact that H() 0 for not belonging to the interval (-2,2). Find the impulse response function h(t) from H() found above. Is...
(1 point) Find y as a function of t if y-8y = 0, (0) - 6, (1) = 2. y(t) Remark The initial conditions involve values at two points
Use Variation of Parameters to solve the following differential equations 4) y" + 8y' +16y = e-45 ln(2)
4- Find unit impulse response for: y(t) + 4у(t) + 3y(t)-x(t) + 5x(t) 5- Find the total response for: ý(t) 13(t) 22y(t)-(t) +5x(t) x(t) e-Stu(t) With the initial condition y(0) 2 and y(0)-3 Identify the natural and forced response of the system. 6- Find the total response for: y(t) +2y(t) 17y(t) 4x(t) 8x(t) x(t) = e-Hu(t)
Solve the initial value problem y" + 8y' + 16y = 0, y(-1) = 2, y' (-1) = 5. Equation Editor Common 2 Matrix o @ sin(a) seca) s in-(a) cos(a) csca) cosa tan(a) cota) tana) Va Va la U yt) =
For the system below find the impulse response. (16 points) y''t+10y't+16yt=3x(t)
x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z). x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z).
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of a WSS process. Find its transfer function (v).
(1 point) Find y as a function of tif y" - 16y=0, y(0) = 5, y(1) = 6. s(t) = Remark. The initial conditions involve values at two points