Test on LTI Systems: Frequency Domain Analysis

Question 1: When an analytic sinusoidal signal is input to an LTI system, the output signal always has a different frequency than the input signal.

A. Ano

B. Ne

Explanation: If the input signal of an LTI system is an analytic sinusoid, the output is also an analytic sinusoid with the same frequency. The output signal's amplitude is weighted, and its initial phase is shifted, but its frequency remains the same as the input.

Question 2: According to the study materials, which statements accurately describe a continuous-time analytic sinusoidal signal?

A. It is a real-valued signal that naturally exists.

B. It is a complex-valued sinusoid more suitable for analysis.

C. It can be represented by two plots in Cartesian coordinates: its real and imaginary parts.

D. It is characterized by amplitude A, angular frequency ω, and period T.

Explanation: The study materials state that the analytic sinusoidal signal is a 'Complex - valued sinusoid – artificial sinusoidal signal version more suitable for analysis.' It also mentions that it can be plotted using 'Cartesian coordinates, two plots: real and imaginary part'. Option 0 is incorrect because the material describes it as complex-valued, not real-valued, and artificial, not naturally existing. Option 3 describes the characterization of a *real-valued* sinusoidal signal, not specifically the analytic one, which is given by A, ω, and initial phase ϕ.

Question 3: When calculating the output signal of an LTI system, the response obtained using a time-domain computation function like MATLAB 'filter()' or Python 'lfilter' is identical to the response obtained using the frequency response method for all time instances.

A. Ano

B. Ne

Explanation: The study materials state that the calculated response from a time-domain computation differs from the response obtained using the frequency response. This difference is due to a transient region caused by the time-domain computation skipping the 'left' part of the input signal.

Question 4: In the MATLAB example provided for plotting a frequency response graph, the `plot(Omega, abs(K))` command is used to visualize the magnitude of the frequency response.

A. Ano

B. Ne

Explanation: The study materials explicitly show `plot(Omega, abs(K))` as the command used to generate the graph for the magnitude of the frequency response K versus Omega in the example.

Question 5: For a linear time-invariant (LTI) system with an input signal given by x[n] = A e^(jΩn), what is the form of the output signal y[n]?

A. y[n] = K_hat(Ω) e^(jΩn)

B. y[n] = A K_hat(Ω) e^(jΩn)

C. y[n] = A e^(jΩn) + K_hat(Ω)

D. y[n] = A K_hat(Ω)

Explanation: According to the study materials, when the input signal to a linear system is x[n] = A e^(jΩn), the output signal is given by y[n] = A K_hat(Ω) e^(jΩn), where K_hat(Ω) represents the frequency response of the system.