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2. Consider the same signal x(t) shown above in question...
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier...
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier series for x(t) and y). b) Sketch the amplitude and phase spectra for signal x(). c) Use Parseval's theorem to approximate the power of the periodic signal x() by calculating the power of the first N harmonics, such that the strength of the Nth harmonic is 10% or more of the power of the DC component.
Q1) For the periodic signals x()...
Q2 Consider a communication signal x(t) described by the following mathematical expression: x(t)=2 cos(2000) + 4...
Q2 Consider a communication signal x(t) described by the following mathematical expression: x(t)=2 cos(2000) + 4 sin? (2000) – 2+4rec(t)cos(6000mt) Analyse the communication signal x(t) then consider the following: (i) Determine the Fourier transform of the signal x(t). (ii) Plot the double-sided amplitude spectrum of the signal x(t).
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[...
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
MATLAB Q1 A signal x(t) is shown in the following figure: X) 3 -2 1 01...
MATLAB
Q1 A signal x(t) is shown in the following figure: X) 3 -2 1 01 2 3 sketch x( t+2).
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Consider the following continuous-time signal. x(t) = 1 for m < t < m + 1...
Consider the following continuous-time signal. x(t) = 1 for m < t < m + 1 −1 for m + 1 < t < m + 2 for m = − 4,−2, 0, 2, 4, · · · Sketch the following signals. (a) x(t) (b) y(t) = 2x(2t − 1) + 1
Question #5: Consider the continuous-time signal shown below. x(t) -6 -4 -2 4 -2 (a) Sketch...
Question #5: Consider the continuous-time signal shown below. x(t) -6 -4 -2 4 -2 (a) Sketch y(t) x1) (b) Sketch y(t) 2x[t- 2) (c) Sketch y(t) - 5x(t/3) (d) Sketch y(t) x(t) -x(-t)
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10...
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Q1. The signal x(t) shown in Figure Q1 is zero except as shown. [No Partial Credit]...
Q1. The signal x(t) shown in Figure Q1 is zero except as shown. [No Partial Credit] x(t) 2 1 -1 0 1 2 3 4 5 t Figure Q1 Clearly indicate the significant points in the time axis and y-axis. a) Plot x(t + 2) b) Plot x(2t - 3) c) Plot x(2-t) [2 marks) [2 marks] [2 marks]
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier series for x(t) and y). b) Sketch the amplitude and phase spectra for signal x(). c) Use Parseval's theorem to approximate the power of the periodic signal x() by calculating the power of the first N harmonics, such that the strength of the Nth harmonic is 10% or more of the power of the DC component.
Q1) For the periodic signals x()...
Q2 Consider a communication signal x(t) described by the following mathematical expression: x(t)=2 cos(2000) + 4 sin? (2000) – 2+4rec(t)cos(6000mt) Analyse the communication signal x(t) then consider the following: (i) Determine the Fourier transform of the signal x(t). (ii) Plot the double-sided amplitude spectrum of the signal x(t).
Q2.) Consider the sampling of the continuous-time signal x(t) to obtain a discrete-time signal x[n (1)-10cos(1000m + π/3) + 20cos(2000m + π/6). 110points! ], where x a) What is the maximum sampling interval (minimum sampling frequency) that could be used to ensure an aliasing free sampling of this signal? b) Plot the spectrum of the sampled signal if x() is sampled using a sampling frequency of (i) 2500 Hz (ii) 1800 Hz and state whether there will be an aliasing...
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
MATLAB
Q1 A signal x(t) is shown in the following figure: X) 3 -2 1 01 2 3 sketch x( t+2).
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Question #5: Consider the continuous-time signal shown below. x(t) -6 -4 -2 4 -2 (a) Sketch y(t) x1) (b) Sketch y(t) 2x[t- 2) (c) Sketch y(t) - 5x(t/3) (d) Sketch y(t) x(t) -x(-t)
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Q1. The signal x(t) shown in Figure Q1 is zero except as shown. [No Partial Credit] x(t) 2 1 -1 0 1 2 3 4 5 t Figure Q1 Clearly indicate the significant points in the time axis and y-axis. a) Plot x(t + 2) b) Plot x(2t - 3) c) Plot x(2-t) [2 marks) [2 marks] [2 marks]
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