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(30 points) (a) Determine the Fourier series for the signal below. (b) Determine Vims for the...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series ...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To ii. What is the average or dc value of x(t)? iii. Is x(t) even, odd, or neither even nor odd function of time? iv. One of the frequency components of x(t) is expressed as Acos(ST) 0- What is A? (b) A train of...
Please provide clear, correct, and detailed answer. WIll rate. 4. The exponential Fourier series of a...
Please provide clear, correct, and detailed answer. WIll
rate.
4. The exponential Fourier series of a periodic signal x(t) of fundamental period To is (a) Determine the value of the fundamental period To (b) What is the average or dc value of r(t)? (c) Is (t) even, odd, or neither? (d) One of the frequency components of x(t) is expressed as a cos(3Tt). What is a?
2. (12 points) Apply the result from part 1 to determine the response of a lowpass...
2. (12 points) Apply the result from part 1 to determine the response of a lowpass filter. a) (4 points) Determine the fundamental frequency and non-zero complex exponential Fourier series coeffi- cients of the periodic signal 2π f(t) =-2-5 sin(2nt) + 10 cos(Grt + "") and sketch the Fourier magnitude spectum D versus w and the Fourier phase spectrum LD versus w (b) (2 points) Use Parseval's theorem for the exponential Fourier series to find the power of the signal...
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()...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even va...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even values of k. Note: You can not use the half-wave symmetry integrals if the half-wave symmetry is "hidden" (i.e. if there is a DC offset).] xft) Signal i x(t) Signal5 x(t) Signal 4 aeP O80 0.5 -1 4 8 I 2 4
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the...
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the exponential Fourier series representation f(t) = Σ Dnejuont . where wo 2T/To and 1. (2 points) When f(t) is a real-valued, show that DD This is known as the complex conjugate symmetry property or the Hermitian property of real signals. 2. (2 points) Show that when f(t) is an even function of time that Dn is an even function of n 3. (2 points)...
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 Cn, θ.) 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 has a...
Is (20 points) The complex exponential Fourier series of a signal xt) over 0<t<T is given...
Is (20 points) The complex exponential Fourier series of a signal xt) over 0<t<T is given as shown below. icos nas x(t)= (a) Calculate the period T (b) Determine the average value of x(1) (C) Find the amplitude of the fifth harmonic,
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To ii. What is the average or dc value of x(t)? iii. Is x(t) even, odd, or neither even nor odd function of time? iv. One of the frequency components of x(t) is expressed as Acos(ST) 0- What is A? (b) A train of...
Please provide clear, correct, and detailed answer. WIll
rate.
4. The exponential Fourier series of a periodic signal x(t) of fundamental period To is (a) Determine the value of the fundamental period To (b) What is the average or dc value of r(t)? (c) Is (t) even, odd, or neither? (d) One of the frequency components of x(t) is expressed as a cos(3Tt). What is a?
2. (12 points) Apply the result from part 1 to determine the response of a lowpass filter. a) (4 points) Determine the fundamental frequency and non-zero complex exponential Fourier series coeffi- cients of the periodic signal 2π f(t) =-2-5 sin(2nt) + 10 cos(Grt + "") and sketch the Fourier magnitude spectum D versus w and the Fourier phase spectrum LD versus w (b) (2 points) Use Parseval's theorem for the exponential Fourier series to find the power of the signal...
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()...
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series Coefficients a, b and XTk] for the following periodic repeating signals. Where appropriate, simplify the results for odd or even values of k. Note: You can not use the half-wave symmetry integrals if the half-wave symmetry is "hidden" (i.e. if there is a DC offset).] xft) Signal i x(t) Signal5 x(t) Signal 4 aeP O80 0.5 -1 4 8 I 2 4
3) (Symmetries and Fourier Coefficients) Compute the Fourier Series...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the exponential Fourier series representation f(t) = Σ Dnejuont . where wo 2T/To and 1. (2 points) When f(t) is a real-valued, show that DD This is known as the complex conjugate symmetry property or the Hermitian property of real signals. 2. (2 points) Show that when f(t) is an even function of time that Dn is an even function of n 3. (2 points)...
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 Cn, θ.) 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 has a...
Is (20 points) The complex exponential Fourier series of a signal xt) over 0<t<T is given as shown below. icos nas x(t)= (a) Calculate the period T (b) Determine the average value of x(1) (C) Find the amplitude of the fifth harmonic,
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