Discrete-Time Impulse and Step Functions. Calculate sigma_n = -infinity^infinity n^2 delta [n – 3] Sketch the function x[n] = n^2 delta [n – T] for T = 0, 1, …, 4 Show that u[n] = sigma_k = -infinity^infinity u[k] delta [n – k] Show that for all functions x[n], x[n] = sigma_k = -infinity^infinity x[k] delta [n – k] Signal and System Properties. State whether each of the statements is true or false. Note that a statement is true if it is always true, without further qualifications. If the statement is false, produce a counterexample to it. If a continuous-time signal is periodic with period T (where T > 0), then it is also periodic with period 2T. Let y(t) be the output of a continuous-time linear system for the input x(t). Then the output of the system for the input 2x(t) is 2y(t). Let y(t) be the output of a continuous-time linear system for the input x(t). Then the output of the system for the input x(t + 1) is y(t + 1). If the input x(t) of a stable continuous-time linear system satisfied |x(t)| Show transcribed image text