Homework Answers
https://www.desmos.com/calculator/lab9nylxsi
For plotting we need to use a software. I have used Desmos since it is free.
I have plot the graph.please click on the above link.
One can change the value of "a" from 10 to 100 to 1000 to get different graphs.
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Problem 1: Find the Fourier series for the following function Plot the series using 10 terms, 20 terms and 100 terms...
I. Find the Fourier series of the following function with period 2π and accurately plot the...
I. Find the Fourier series of the following function with period 2π and accurately plot the first three partial sums. [10 points f(x) A -π -π/2 0 π/2 π
(20 points) Consider the function f(z) z in the interval [0, 2π). (a) Derive the Fourier...
(20 points) Consider the function f(z) z in the interval [0, 2π). (a) Derive the Fourier coefficients ck fork = 0, 1,土2, (b) Derive the Fourier coefficients ao, ak, bk for k 1,2,... .. (c) Plot the partial Fourier series, along with the function f, by retaining 1, 10, 50, 100 terms in the summation (use the second form involving cosines and sines) d) Comment on the convergence of the partial Fourier series. Note: you should submit only 1 plot...
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<...
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and the first three partial sums of the Fourier series S1, S2, S3 on the same plot. Partial sum...
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and the first three partial sums of the Fourier series S1, S2, S3 on the same plot. Partial sum Sn is the sum of all contributions from the frequencies less than or equal to n, i.e. Sn(x) = a0+ Σ 1 (ak cos(kx) +br sin(kx))
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and...
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0 <...
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0 < x < 4 Using notation similar to Problem # 2 above, (a) Find the value of co. (b) Find the function g1(n, x). (c) Find the function g(n, x).
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0
Problem 3: Derive the Fourier series for the function f(x) = x + (1/2) for −1...
Problem 3: Derive the Fourier series for the function f(x) = x + (1/2) for −1 < x < 1; plot the function and its Fourier series for −3 < x < 3
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
(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 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...
Using MATLAB (a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs...
Using MATLAB
(a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs1. T-2 (b) Using MATLAB, plot the first 20 terms and the first 200 terms of the Fourier series in the interval -3< r<3, In order to do this, the r-interval should be divided into 6001 cqually spaced points by making use of the MATLAB command linspace.
(a) Find the Fourier series for 25 { O if 1...
I. Find the Fourier series of the following function with period 2π and accurately plot the first three partial sums. [10 points f(x) A -π -π/2 0 π/2 π
(20 points) Consider the function f(z) z in the interval [0, 2π). (a) Derive the Fourier coefficients ck fork = 0, 1,土2, (b) Derive the Fourier coefficients ao, ak, bk for k 1,2,... .. (c) Plot the partial Fourier series, along with the function f, by retaining 1, 10, 50, 100 terms in the summation (use the second form involving cosines and sines) d) Comment on the convergence of the partial Fourier series. Note: you should submit only 1 plot...
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<...
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and the first three partial sums of the Fourier series S1, S2, S3 on the same plot. Partial sum Sn is the sum of all contributions from the frequencies less than or equal to n, i.e. Sn(x) = a0+ Σ 1 (ak cos(kx) +br sin(kx))
Find Fourier coefficients for the following function defined on x E [-π, π] Plot the original function and...
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0 < x < 4 Using notation similar to Problem # 2 above, (a) Find the value of co. (b) Find the function g1(n, x). (c) Find the function g(n, x).
Problem #5: Expand the following function in a Fourier series of period 4. fx5x27x, 0
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
(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 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...
Using MATLAB
(a) Find the Fourier series for 25 { O if 1 r<O 1-2 if 0<H<1 f(x) defined on the interval -1<rs1. T-2 (b) Using MATLAB, plot the first 20 terms and the first 200 terms of the Fourier series in the interval -3< r<3, In order to do this, the r-interval should be divided into 6001 cqually spaced points by making use of the MATLAB command linspace.
(a) Find the Fourier series for 25 { O if 1...
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