Answer Happy

1. [24 points] Please answer the following short answer questions. a. [4 pts] Determine the properties of the discrete time signal x[n]u[n + 4] - u[n - 5]. i. Even/Odd ii. Periodic/Aperiodic iii. Energy/Power/Neither iv. Causal/Anticausal/Noncausal s(™) +²cos (n) periodic? b. [4 pts] Is the signal y[n] = COS c. [4 pts] Consider a discrete-time signal x[n] = 3n u[n]. i. What is its z-transform and the Region of Convergence (ROC)? ii. What is the z-transform of 3" x[n - 2]?
d. [4 pts] What is the region of convergence (ROC) for a causal signal with z- transform X(z) = 1 (z²-6z+25) -? = e. [4 pts] If the Nyquist rate for sampling the band limited real signal x (t) is w₁ 10 rad/sec, then what is the Nyquist rate for sampling x(t)cos (20t) ? f. [4 pts] Please mark whether the following statements are true or false. i. If a continuous time signal's length is shrunk in time domain, the length of its Fourier Transform will increase in the frequency domain. (T/F) ii. If the amplitude of a continuous time signal is doubled, the magnitude of its Fourier Transform will also be doubled. (T/F)