2. (21 pts) Given the general properties listed in Problem #1, determine which ones hold and which ones do not hold for the following discrete-time systems. Justify your answers. Like before, y[n] denotes system output and r[n] is the system input.

Given point (0,0,1) in the right image, what is the equation of the correspondingepipolar line in the left image? Enter A,B,C or D. A) -10 y + 20 = 0 B)-100 x + 20 = 0 C) 10 x + 20 y + 100 = 0 D) -10 x + 20 y + 100 = 0

Discrete Fourier Transform (DFT) (10 pts) Find an expression for the DFT, X[k], When the input sequence is defined by x[n] = {1, 0, 1, 0} then determine the

6) Determine whether the following systems are invertible: (a) y(t) = x(-t) and (b) y(t) =tx(t)

2. Use the table below to calculate the Apartment's Energy Consumption for each day:(34 Express the energy consumption in kilo-Watt-Hour (kWh): W = 47582.7 * 0.25 =11895.675

Determine the Fourier-series expansion of the following signals: \text { 1. } x(t)=\cos (2 \pi t)+\cos (4 \pi t) \text { 2. } x(t)=\cos (2 \pi t)-\cos (4 \pi t+\pi / 3) \text { 3. } x(t)=2 \cos (2 \pi t)-\sin (4 \pi t) \text { 4. } x(t)=\sum_{n=-\infty}^{\infty} \Lambda(t-2 n)

1. A continuous-time signal x(t) is shown in Figure below. Sketch and label carefully each of the following signals: (а) x(- 1) (b) x(2- t) (c) x(2t + 1)

Convert each signal to the finite sequence form {a, b, c, d, e}. \text { (b) } n \cdot u[n]-n \cdot u[n-5] \text { (c) } u[n-1] \cdot u[4-n] \text { (d) } 2 \delta[n-1]-4 \delta[n-3] \text { (а) } \quad u[n]-\delta[n-3]-u[n-4]

Consider a pulse s(t) = sinc(at)sinc (bt). where a z b. (a) Sketch the frequency-domain response S(f) of the pulse. (b) Suppose that the pulse is to be used over an ideal real-base band channel with one-sided bandwidth 400 Hz. Choose a and b so that the pulse is Nyquist for 4PAM signaling at 1200 bits/s and exactly fills the channel bandwidth. (c) Now, suppose that the pulse is to be used over a passband channel spanning the frequency range 2.4-2.42 GHz. Assuming that we use64QAM signaling at 60 Mbits/s, choose a and b so that the pulse is Nyquist and exactly fills the channel bandwidth. (d) Sketch an argument showing that the magnitude of the transmitted waveform in the preceding settings is always finite.

(a) Given the second-order frequency response function: H(j \omega)=\frac{100}{(j \omega)^{2}+51 j \omega+50} (i) Analytically determine the straight line approximations (asymptotes) of the Bode Log-Magnitude plot of the frequency response function. (ii) Sketch the Bode magnitude (dB) of the frequency response function, clearly labeled, and indicate the frequency () where the OdB-line is crossed on your sketch. You are not required to sketch the phase. An LTI system subjected to an input x() has a response y(t), and its frequency response function is: H(j \omega)=\frac{2}{\frac{1}{3}(j \omega)^{2}+\frac{5}{3} R j \omega+2} \text { where } R \text { is a resistance }(\Omega) \text {. } For what range of values of the resistance R is the system under damped? \text { (ii) If } R=1 \Omega \text {, what is the impulse response, } h(t) \text { of the system? } \text { (ii) If } R=1 \Omega \text {, what is the impulse response, } h(t) \text { of the system? } \text { (iii) If } R=1 \Omega \text {, what is the step response, } s(t) \text { of the system? }