Only e and f; thank you

Using MATLAB signals and systems

textbook: computer explorations in signals and systems using Matlab

I 3.9 Frequency Response of a Continuous-Time System This exercise demonstrates the effect of the frequency response of a continuous-time system on periodic signals. You will examine the response of a simple linear system to each of the harmonics that compose a periodic signal as well as to the periodic signal itself. In this exercise you will need to use the function lsim as discussed in the Tutorial 3.3. Consider a simple RC circuit that has a system function given by H(s) 1 1 + RCS whose input is given by x(t) = cos(t), and whose output is y(t). For the problems that follow, use t=linspace(0,20, 1000) for all simulations, and assume that the time constant RC is 1. Intermediate Problems (a). Use the function 1sim to simulate the response of the system H(s) to x(t) over 05 t > x2=cos(t); >> x2(x2>0)=ones (size(x2(x2>0))); >> x2(x2> sl=apos_k(1)*exp(j*t)+aneg_k(1) *exp(-j*t); Construct the signals s1, s2, s3, s4, and s5. Plot the sum of these signals on the same graph as the square wave x2. (d). Since the circuit is linear, the response of the system to the square wave input can be calculated by finding the response of the system to each harmonic component separately, and then summing the results. Verify this by using lsim to find the responses y 1, y5 to the signals s1, ..., s5 as well as the response of the system to the signal ssum which is the sum of the first five harmonic components, s1 through s5. (e). Compare the response of the system to the sum of the first 5 harmonics to the response of the system to the original square wave. Can you explain why the two responses are so similar? Hint: Consider the energy in the CTFS of x2 as a function of the number of coefficients used in the approximation to x2. (f). Verify that your signals yi, y5 are correct by constructing each signal from the system function H(s) and the CTFS for x2. For each, plot both the analytically determined and the simulated signals over 10 > x2=cos(t); >> x2(x2>0)=ones (size(x2(x2>0))); >> x2(x2> sl=apos_k(1)*exp(j*t)+aneg_k(1) *exp(-j*t); Construct the signals s1, s2, s3, s4, and s5. Plot the sum of these signals on the same graph as the square wave x2. (d). Since the circuit is linear, the response of the system to the square wave input can be calculated by finding the response of the system to each harmonic component separately, and then summing the results. Verify this by using lsim to find the responses y 1, y5 to the signals s1, ..., s5 as well as the response of the system to the signal ssum which is the sum of the first five harmonic components, s1 through s5. (e). Compare the response of the system to the sum of the first 5 harmonics to the response of the system to the original square wave. Can you explain why the two responses are so similar? Hint: Consider the energy in the CTFS of x2 as a function of the number of coefficients used in the approximation to x2. (f). Verify that your signals yi, y5 are correct by constructing each signal from the system function H(s) and the CTFS for x2. For each, plot both the analytically determined and the simulated signals over 10