Consider the Fourier Series for the periodic function: x(t) = 4+ 4 cos(5t)+ 6 sin (10t)...
Consider the Fourier Series for the periodic function:
x(t) = 4+ 4 cos(5t)+ 6 sin (10t)
a.) Find the Fourier coefficients of the exponential form.
b.) Find the Fourier Coefficients of the combined trigonometric form.
c.) Sketch the one-sided power spectral density
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Consider the Fourier Series for the periodic function:
x(t) = 4+ 4 cos(5t)+ 6 sin (10t)...
Consider the Fourier series for the periodic function: x(t)= 3 + 5cos t +6 sin (2t)...
Consider the Fourier series for the periodic function: x(t)= 3 + 5cos t +6 sin (2t) a.) Find the Fourier Coefficients of the exponential form b.) Find the Fourier Coefficients of the combined trigonometric form c.) Find the normalized average power using the Fourier series coefficient d.) Sketch the one sided Power Spectral Density
4. Consider the Fourier series for the periodic function given below: x(t) = 3 + 5Cost...
4. Consider the Fourier series for the periodic function given below: x(t) = 3 + 5Cost + 6 Sin(2t + /4) Find the Fourier coefficients of the combined trigonometric form for the signal.
Consider the following DT periodic signal: in X(t) = sin 2πη) 10 + cos 30) a)...
Consider the following DT periodic signal: in X(t) = sin 2πη) 10 + cos 30) a) What is the fundamental period? b) What are the exponential Fourier series coefficients? c) Sketch magnitude and phase spectral plots.
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...
Please show all your works. Thanks. 4.(25 pts) Consider a periodic function X(t) = Sin(3t). Cos...
Please show all your works.
Thanks.
4.(25 pts) Consider a periodic function X(t) = Sin(3t). Cos . Express x(t) in Exponential Fourier Series form and calculate Fourier Coefficients Co, C1, C-1,C2, C-2 ... etc (as many Fourier Coefficients as needed). What is the fundamental frequency (wo) of the x(t)? (hint: Use Euler's formula to express Sin(.) and Cos(.) in exponential forms)
4. A periodic signal x (t) is represented by a trigonometrie Fourier series X(t) = 8...
4. A periodic signal x (t) is represented by a trigonometrie Fourier series X(t) = 8 + 4 cos (2t + 60°) + 2sin (3t+30°) - cos (4t + 150°) = 0 * +30°) - cos (4t+150°) = 3 +4 Cos(216)+2 Cart ( 6) Col413 (a) Sketch the trigonometric Fourier series spectra (both magnitude and phase). O i 2 3 (b) Sketch the exponential Fourier series spectra (both magnitude and phase). + Dol -3 -2 -1 0 1 2 3...
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...
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]....
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
3.11-For each of the following signals compute the complex exponential Fourier series by using tr...
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals
3.11-For each...
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4...
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4 + j3)e-j6t + j3e-j4t + 2 - j3ej4t + (4 - j3) jót a) What is the fundamental frequency? b) By inspection write the signal x(t) in a compact trigonometric form. c) Find the power of the signal.
4. Consider the Fourier series for the periodic function given below: x(t) = 3 + 5Cost + 6 Sin(2t + /4) Find the Fourier coefficients of the combined trigonometric form for the signal.
Consider the following DT periodic signal: in X(t) = sin 2πη) 10 + cos 30) a) What is the fundamental period? b) What are the exponential Fourier series coefficients? c) Sketch magnitude and phase spectral plots.
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...
Please show all your works.
Thanks.
4.(25 pts) Consider a periodic function X(t) = Sin(3t). Cos . Express x(t) in Exponential Fourier Series form and calculate Fourier Coefficients Co, C1, C-1,C2, C-2 ... etc (as many Fourier Coefficients as needed). What is the fundamental frequency (wo) of the x(t)? (hint: Use Euler's formula to express Sin(.) and Cos(.) in exponential forms)
4. A periodic signal x (t) is represented by a trigonometrie Fourier series X(t) = 8 + 4 cos (2t + 60°) + 2sin (3t+30°) - cos (4t + 150°) = 0 * +30°) - cos (4t+150°) = 3 +4 Cos(216)+2 Cart ( 6) Col413 (a) Sketch the trigonometric Fourier series spectra (both magnitude and phase). O i 2 3 (b) Sketch the exponential Fourier series spectra (both magnitude and phase). + Dol -3 -2 -1 0 1 2 3...
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...
1. For each periodic signal below determine its Fourier series coefficients for x E [-π, π]. (Hints: find shortcuts using trigonometric formulas, and note that c can be obtained from a) and b).) rom a an a)() 10t) b) g(t)+cos(2t) c) f(t)1cos(2t) sin(10T) cos(2 sin
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals
3.11-For each...
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4 + j3)e-j6t + j3e-j4t + 2 - j3ej4t + (4 - j3) jót a) What is the fundamental frequency? b) By inspection write the signal x(t) in a compact trigonometric form. c) Find the power of the signal.
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