Consider a CLTI system has the input signal x(t) and the impulse response h(t). Use convolution integral and the analytical method to find the system's output y(t). (a) x(t) = e-2tu(t – 2), h(t) = u(t – 4) (b) x(t) = r(t), h(t) = rect((t – 4)|6)

A signal's spectrum contains four components: -2500 Hz, -1700 Hz, +1700 Hz, and +2500 Hz. If we assume this spectrum is the product of two sinusoidal signals, what are the frequencies of the two signals whose product gives rise to this spectrum? 400 Hz and 2100 Hz 1700 Hz and 2500 Hz 1300 Hz and 2100 Hz 800 Hz and 4200 Hz

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…