Consider the coherent (synchronous) demodulator as shown in the Figure 1. Investigate the following.
Q2 \(\quad\) Consider the coherent (skcronous) demodutor as shown in the Figure 1. Investigate the following.
a) mathematical expressions for \(\mathrm{x}_{1}(\mathrm{t}), \mathrm{x}_{2}(\mathrm{t})\) and \(\mathrm{x}_{3}(\mathrm{t})\).
b) the spectrum of \(\mathrm{x}_{1}(\mathrm{t}), \mathrm{x}_{2}(\mathrm{t})\) and \(\mathrm{x}_{3}(\mathrm{t})\)
c) If \(x_{0}(t)=\cos \left(\right.\) wath in Figure \(1,\) what would be the modified \(x_{1}(t), x_{2}(t)\) and \(x_{3}(t)\).
d) Suppose that, the positions of the two blocks in Figure 1 , i.e., the "Low Pass Filter" and the "dc blocker", are interchanged, what would be the modified mathematical expressions for \(x_{1}(t), x_{2}(t)\) and \(x_{3}(t)\)
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Consider the coherent (synchronous) demodulator as shown in the Figure 1. Investigate the following.
Problem 17. Consider the standard amplitude-modulation system shown in Figure 3 Figure 3 x) Chann...
Analysis Linear Systems
Problem 17. Consider the standard amplitude-modulation system shown in Figure 3 Figure 3 x) Channel Filter he(r) cos wor cos ωοι M(w) H(u) (a) Sketch the spectrum of r(t). (b) Sketch the spectrum of y(t) for the following cases: (i) 0S WcWo-m (iii) wc >wowm (c) Sketch the spectrum of z(t) for the following cases: (i) 0 S WcWo-m (iii) wc >wowm d) Sketch the spectrum of v(t) if we wowm and (i) w
Question 10 (10pts.): Use the figure below, Explain all answers 1) which spectrum would be best...
Question 10 (10pts.): Use the figure below, Explain all answers 1) which spectrum would be best to create a DC power supply? What kind of filter would you us 2) Which spectrum would you use to create a 10kHz carrier wave Figure I Spectrum Signal Figure 2: Spectrm Signol2 Figure 3: Spectrum Signal
ANSWER ALL THE QUESTIONS Question 1 For the circuit shown in Figure Q1, select a value...
ANSWER ALL THE QUESTIONS Question 1 For the circuit shown in Figure Q1, select a value of R so that the energy stored in the inductor is equal to the energy stored in the capacitor at steady state. 22 Ω 10mH 15v (t Figure Q1 (5 marks) Question 2 For the network in Figure Q2. (a) Find the mathematical expressions for the voltage yz and the current ic following the (9 marks) (4 marks) closing of the switch. (b) Sketch...
h(t) h(1) + ht) Figure Q2 (a) Q2 (a) Consider the system shown in Figure Q2...
h(t) h(1) + ht) Figure Q2 (a) Q2 (a) Consider the system shown in Figure Q2 (a). Find the overall impulse response of the system, h(t) with impulse responses given below. h(t) = 3e-Stu(t) hy(t) = et u(t) hg(t) = 2t u(t) (5 marks) (b) Determine whether the system, h(t) obtained in Q2 (a) is: (1) Stable (3 marks) (ii) Causal (2 marks) Q3. (a) Explain the Gibbs phenomenon. (3 marks) (b) Given a signal 3 x(t) = x+7cos (41t+...
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20...
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
Design a synchronous sequential counter circuit that has the state diagram shown in figure 1. Use...
Design a synchronous sequential counter circuit that has the state diagram shown in figure 1. Use both D-type and T-type Flip Flops in your design. Show all your work in details. Extra credit will be given for implementation using other types of Flip Flops 3 4 Figure 1 Deliverables: 1. State Transition Table 2. K-Maps 3. Logical Expressions (Minimal Form) 4. Schematic Diagrams of the two designs 5. Verification steps for both designs.
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2...
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2 2 a. I (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(...
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
Analysis Linear Systems
Problem 17. Consider the standard amplitude-modulation system shown in Figure 3 Figure 3 x) Channel Filter he(r) cos wor cos ωοι M(w) H(u) (a) Sketch the spectrum of r(t). (b) Sketch the spectrum of y(t) for the following cases: (i) 0S WcWo-m (iii) wc >wowm (c) Sketch the spectrum of z(t) for the following cases: (i) 0 S WcWo-m (iii) wc >wowm d) Sketch the spectrum of v(t) if we wowm and (i) w
Question 10 (10pts.): Use the figure below, Explain all answers 1) which spectrum would be best to create a DC power supply? What kind of filter would you us 2) Which spectrum would you use to create a 10kHz carrier wave Figure I Spectrum Signal Figure 2: Spectrm Signol2 Figure 3: Spectrum Signal
ANSWER ALL THE QUESTIONS Question 1 For the circuit shown in Figure Q1, select a value of R so that the energy stored in the inductor is equal to the energy stored in the capacitor at steady state. 22 Ω 10mH 15v (t Figure Q1 (5 marks) Question 2 For the network in Figure Q2. (a) Find the mathematical expressions for the voltage yz and the current ic following the (9 marks) (4 marks) closing of the switch. (b) Sketch...
h(t) h(1) + ht) Figure Q2 (a) Q2 (a) Consider the system shown in Figure Q2 (a). Find the overall impulse response of the system, h(t) with impulse responses given below. h(t) = 3e-Stu(t) hy(t) = et u(t) hg(t) = 2t u(t) (5 marks) (b) Determine whether the system, h(t) obtained in Q2 (a) is: (1) Stable (3 marks) (ii) Causal (2 marks) Q3. (a) Explain the Gibbs phenomenon. (3 marks) (b) Given a signal 3 x(t) = x+7cos (41t+...
1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
Design a synchronous sequential counter circuit that has the state diagram shown in figure 1. Use both D-type and T-type Flip Flops in your design. Show all your work in details. Extra credit will be given for implementation using other types of Flip Flops 3 4 Figure 1 Deliverables: 1. State Transition Table 2. K-Maps 3. Logical Expressions (Minimal Form) 4. Schematic Diagrams of the two designs 5. Verification steps for both designs.
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2 2 a. I (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
just looking for #2, 3, and 4
Problems: 1. Consider the system shown below. Let the input signal to the Ideal Sampler to be: s(t) = 2 cos(2m50t) + 4cos(2m100t) a. (10 points) Determine S(f) and plot it b. (20 points) Let the sampling rate to be: fs 300 samples/sec. Plot the spectrum of the Ideal sample, that is plot S8(f) c. Let the sampling rate to be: fs 175 samples/sec. i. (30 points) Plot S8(f) ii. (10 points) Let...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
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