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Problem 1: Consider the continuous-time signal r(t) as shown in Figure 1. r(t) Figure 1: A...
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and...
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the spectral line. [2 Find the fundamental frequency and identilY the harmonics in the signal. 12) Solution
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
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...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%]...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1...
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1 3 2 - - 1 1 0 1 2 3 4 5 6 t A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N....
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
6- A continuous-time periodic signal r(t) is given graphically below (a) Determine the exponential Fourier coefficients...
6- A continuous-time periodic signal r(t) is given graphically below (a) Determine the exponential Fourier coefficients c for k+oo r(t) Cet k=-oo where ck is given by T/2 x(t)ejkwotdt -T/2 Ск T (b) (t) is applied as an input to an LTI system whose frequency response is H(jw)2 sin(w) = Determine the corresponding output y(t) (c) Sketch y(t). Be re to mark the ces properly su x(t)t 0 -T
6- A continuous-time periodic signal r(t) is given graphically below (a)...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquis...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquist rate to get the sequence r[n]. (a) Sketch X(e) (b) If y[n] = [4n]. Sketch Y(e'"). (c) Is there any aliasing in the Fourier spectrum of yin]? Why or Why Not? (d) If z [n] = x-1, ketch the DTFT of z[n] (e) Is there any aliasing in the Fourier spectrum of [n]? Why or Why Not?
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is...
1. (25 points) A continuous-time periodic signal x (t) is real valued and has a fundamental...
1. (25 points) A continuous-time periodic signal x (t) is real valued and has a fundamental period T-8. The nonzero Fourier series coefficients for x(t) are Express x(t) in the fornm
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the spectral line. [2 Find the fundamental frequency and identilY the harmonics in the signal. 12) Solution
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
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...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
4. (20 points) Consider the periodic signal z(t) shown in the Figure below: x(t) 1 1 3 2 - - 1 1 0 1 2 3 4 5 6 t A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
20 points) Consider the periodic signal z(t) shown in the Figure below: X(t) 3 2 N. 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
6- A continuous-time periodic signal r(t) is given graphically below (a) Determine the exponential Fourier coefficients c for k+oo r(t) Cet k=-oo where ck is given by T/2 x(t)ejkwotdt -T/2 Ск T (b) (t) is applied as an input to an LTI system whose frequency response is H(jw)2 sin(w) = Determine the corresponding output y(t) (c) Sketch y(t). Be re to mark the ces properly su x(t)t 0 -T
6- A continuous-time periodic signal r(t) is given graphically below (a)...
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is sampled at twice the Nyquist rate to get the sequence r[n]. (a) Sketch X(e) (b) If y[n] = [4n]. Sketch Y(e'"). (c) Is there any aliasing in the Fourier spectrum of yin]? Why or Why Not? (d) If z [n] = x-1, ketch the DTFT of z[n] (e) Is there any aliasing in the Fourier spectrum of [n]? Why or Why Not?
3. The signal continuous time signal re(t)-cos(200t)2cos cos(100t) is...
1. (25 points) A continuous-time periodic signal x (t) is real valued and has a fundamental period T-8. The nonzero Fourier series coefficients for x(t) are Express x(t) in the fornm
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