Post on 12-Jan-2016
Fourier Series and Fourier Series and TransformsTransforms
Clicker questionsClicker questions
Does the Fourier series of the function f converge at x = 0?
0%0%
1. Yes2. No
0 if
4
0 if4)(
x
xxf
0 of 510
To what value does the Fourier series of the function f converge at x = 0?
0% 0%0%
0 if
4
0 if4)(
x
xxf
0 of 510
1. 02. – /43. /4
To what value does the Fourier series of the function f converge at x = 1?
0% 0%0%
0 if
4
0 if4)(
x
xxf
0 of 510
1. 02. – /43. /4
To what value does the Fourier series of the function f converge at x = ?
0% 0%0%
0 if
4
0 if4)(
x
xxf
0 of 510
1. 02. – /43. /4
What is the value of the coefficient a3 in the cosine half-range expansion of the function f(x) = 1 on the
interval [0, 1]?
0% 0%0%0%
1. 12. 23. 04. /2
0 of 510
What is the value of the coefficient b3 in the cosine half-range expansion of the function f(x) = 1 on the
interval [0, 1]?
0% 0%0%0%
1. 12. 23. 04. /2
0 of 510
What is the value of the coefficient a0 in the cosine half-range expansion of the function f(x) = 1 on the
interval [0, 1]?
0% 0%0%0%
1. 12. 23. 04. /2
0 of 510
What is the value of the coefficient b1 in the sine half-range expansion of the function f(x) = 1 on the
interval [0, 1]?
0% 0%0%0%
0 of 5
1. 1/2. 4/3. 04. /2
10
What is the Fourier transform of f ’’?
0% 0%0%0%
)(ˆ kf1. - k
2. - k2
3. -i k2
4. k2
)(ˆ kf
)(ˆ kf
)(ˆ kf
100 of 5
What is the Fourier transform of the following function?
0% 0%0%
0 if0
0 if)exp()(
x
xaxxf
ikakf
1
)(ˆ1.
)(21
)(ˆika
kf
2.
)(21
)(ˆika
kf
3.
0 of 510
What is the sine Fourier transform, , of f ’?
0% 0%0%
10
)(' kfs
)( kfk s1.
)( kfk c2.
)0(2
)( fkfk s
3.
0 of 5
What is the cosine Fourier transform, , of f ’?
0% 0%0%
10
)(' kfc
0 of 5
)( kfk s1.
)( kfk c2.
)0(2
)( fkfk s
3.