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Question 1 Find the Fourier series representation of the periodic function below if p = 15...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 15...
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 151, showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n = 5 and n = 20 terms.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier...
Find the Fourier series representation (give 4 nonzero terms-include at least one cosine term and one...
Find the Fourier series representation (give 4 nonzero terms-include at least one cosine term and one sine term if both exist) of the following periodic function which in one period is given by: -2<x<0. f= 0 0<x<2 f = 1 2 A Avot w To 2 Find the Fourier series representation (give 4 nonzero terms-include at least one cosine term and one sine term if both exist) of the following periodic function which in one period is given by: -1<x<T...
Q#2 (22 points) (a) Find the Fourier series of the function by expanding the function as...
Q#2 (22 points) (a) Find the Fourier series of the function by expanding the function as an odd periodic function with a period of 10 units, as shown in Figure below. Plot the first, second, third and fourth partial sums of this Fourier series between -5 to +5 (Matlab is preferable). There will be single graph with 4 plots (b) Draw the amplitude versus frequency spectrum for first four non-zero terms of the Fourier series. Note that y(t) for -5<t<...
-Let-f(t)= 10 +:īncos nuot ot Could f(t) be the Fourier series representation of the periodic function...
-Let-f(t)= 10 +:īncos nuot ot Could f(t) be the Fourier series representation of the periodic function shown below? Use qualitative reasoning only, i.e., do not attempt to find the Fourier series coefficients in answering this question. Justify your answer
For the periodic function below find the as, a, and bi coefficients in the Fourier series...
For the periodic function below find the as, a, and bi coefficients in the Fourier series expansion. (20 points) 0
Find a Fourier series representation in the form x(t)-xp ol + 〉 2 KI k ||...
Find a Fourier series representation in the form x(t)-xp ol + 〉 2 KI k || cos(kat+ X | k |) of a. に! the impulse train and plot the spectrum of the series through the 5th harmonic. Write out the first five terms of the Fourier series of x(t) b. Now, find a Fourier series representation in the form x(t)=X[0] +Σ2k[k] cos(kay + X[k]) of the following (periodic) square wave に! 0 To To/2 To and plot the spectrum...
2. Calculate the exponential Fourier series representation of the periodic function f(t) graphed below. Each arrow...
2. Calculate the exponential Fourier series representation of the periodic function f(t) graphed below. Each arrow in the figure is a Dirac Delta function (two are indicated as examples): 1.20 1.00 0.80 0.60 1 5 (t) 5(-3) 0.40 LLLLLLLLLLLLL 0.20 0.00 -2 -1 0 1 2 3 4 5 6 7
Write the Fourier series representation for each periodic func- tion. One period is defined for e...
Please do 1,3,4,5,6
Write the Fourier series representation for each periodic func- tion. One period is defined for each. Express the answer as a series f(t) = 1, using the summation symbol. Problem 7 of Section 7.2 Problem 8 of Section 7.2 Problem 9 of Section 7.2 Problem 11 of Section 7.2 Problem 14 of Section 7.2 9. 10. 11. 12. 13. f(t) = t + 2π, -2π < t < 2π 4. ft) 5. Use Maple to compute the...
(1 point) Book Problem 15 Follow the steps below to find a power series representation for...
(1 point) Book Problem 15 Follow the steps below to find a power series representation for the function f(0) = ln(8 - x): a) A power series for t... (first 3 non-zero terms) - b) Observe that In(8 - 2) = | !!! dac c) The function f(x) = ln(8 - x) = +... (first 3 non-zero terms).
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier coefficients for the function f(x)-9, 0, TL b. Use the computer to draw the Fourier sine series of f(x), for x E-15, 151, showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n = 5 and n = 20 terms.
(1 point) Consider the Fourier sine series: ) 14, sin( f(z) a. Find the Fourier...
Find the Fourier series representation (give 4 nonzero terms-include at least one cosine term and one sine term if both exist) of the following periodic function which in one period is given by: -2<x<0. f= 0 0<x<2 f = 1 2 A Avot w To 2 Find the Fourier series representation (give 4 nonzero terms-include at least one cosine term and one sine term if both exist) of the following periodic function which in one period is given by: -1<x<T...
Q#2 (22 points) (a) Find the Fourier series of the function by expanding the function as an odd periodic function with a period of 10 units, as shown in Figure below. Plot the first, second, third and fourth partial sums of this Fourier series between -5 to +5 (Matlab is preferable). There will be single graph with 4 plots (b) Draw the amplitude versus frequency spectrum for first four non-zero terms of the Fourier series. Note that y(t) for -5<t<...
-Let-f(t)= 10 +:īncos nuot ot Could f(t) be the Fourier series representation of the periodic function shown below? Use qualitative reasoning only, i.e., do not attempt to find the Fourier series coefficients in answering this question. Justify your answer
For the periodic function below find the as, a, and bi coefficients in the Fourier series expansion. (20 points) 0
Find a Fourier series representation in the form x(t)-xp ol + 〉 2 KI k || cos(kat+ X | k |) of a. に! the impulse train and plot the spectrum of the series through the 5th harmonic. Write out the first five terms of the Fourier series of x(t) b. Now, find a Fourier series representation in the form x(t)=X[0] +Σ2k[k] cos(kay + X[k]) of the following (periodic) square wave に! 0 To To/2 To and plot the spectrum...
2. Calculate the exponential Fourier series representation of the periodic function f(t) graphed below. Each arrow in the figure is a Dirac Delta function (two are indicated as examples): 1.20 1.00 0.80 0.60 1 5 (t) 5(-3) 0.40 LLLLLLLLLLLLL 0.20 0.00 -2 -1 0 1 2 3 4 5 6 7
Please do 1,3,4,5,6
Write the Fourier series representation for each periodic func- tion. One period is defined for each. Express the answer as a series f(t) = 1, using the summation symbol. Problem 7 of Section 7.2 Problem 8 of Section 7.2 Problem 9 of Section 7.2 Problem 11 of Section 7.2 Problem 14 of Section 7.2 9. 10. 11. 12. 13. f(t) = t + 2π, -2π < t < 2π 4. ft) 5. Use Maple to compute the...
(1 point) Book Problem 15 Follow the steps below to find a power series representation for the function f(0) = ln(8 - x): a) A power series for t... (first 3 non-zero terms) - b) Observe that In(8 - 2) = | !!! dac c) The function f(x) = ln(8 - x) = +... (first 3 non-zero terms).
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