3. (20 points) Consider the causal and BIBO-stable LTI system described by the following first order constant coincide deference equation: (a) Determine the system function H(z) and the impulse response h(n), by taking the inverse Z-transform of H(z). (b) Suppose the system is initially relaxed, is applied to the relaxed system. Determine the output y(n) (note that y(n) is the zero-state response of the system). Determine the natural response of the system ynr(n), and the forced response of the system yfr(n). (c) Suppose the system is non-relaxed is applied to the non-relaxed system. Determine the zero-input response of the system yzi(n), the zero-state response of the system yzs(n), and the total response of the system y(n). • (Bonus Problem, 5 points) Based on the pole-zero plot and the ROC of H(z), what type of

6. [Extra Credit] Let x(t)be a real-valued signal carrying the message that we want to deliver, for which . A communication transmitter performs the amplitude modulation to produce the signal The signal g (t)travels from the transmitter to a receiver. Here, we assume there is no path loss or phase distortion, i.e., the signal g(t) is received by the receiver perfectly. At the receiver, the received signal g(t)is demodulated, shown in the following figure. Here, symbol denotes the multiplication operation. The ideal lowpass filter has cutoff frequency of 2,000π and passband gain of 2. Determine the demodulator output y(t). Please list the detail steps to receive full credit [Extra Credit 10 points].