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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 15 Multiple choice questions
Fourier series and transforms
Quiz Content
*
not completed
.
Which of the following is
not
true about the Fourier series?
It provides a useful approximation for periodic functions.
correct
incorrect
The approximated function must be differentiable.
correct
incorrect
Symmetric functions only contain cosine harmonics and a constant term.
correct
incorrect
Antisymmetric functions only contain sine harmonics.
correct
incorrect
*
not completed
.
Which of the following is
not
true about the
complex
Fourier series (of a
real
function)?
It allows the Fourier series to be written in compact notation.
correct
incorrect
The Fourier summation has to be extended to include negative harmonic order.
correct
incorrect
The Fourier coefficients are complex in general.
correct
incorrect
The Fourier coefficients of symmetric functions are imaginary.
correct
incorrect
*
not completed
.
Which of the following is
not
true about Fourier transforms?
They are the limiting integral form of a Fourier series when the repeat period, or wavelength, becomes infinitely large.
correct
incorrect
The Fourier transform and its inverse come as a pair, and which one is called which is arbitrary.
correct
incorrect
The precise definition of a Fourier transform is a matter of convention but, once fixed, its inverse is uniquely defined.
correct
incorrect
The Fourier transform of a real function is real.
correct
incorrect
*
not completed
.
If f(
x
) has a width
w
, or has structure of that characteristic length, what is the corresponding length scale for its Fourier transform F(
k
)?
1/
w
correct
incorrect
w
correct
incorrect
w
^{2}
correct
incorrect
e
^{w}
correct
incorrect
*
not completed
.
Which of the following is
not
a property of convolutions?
The convolution of f(
x
) with g(
x
) is a blurring of f(
x
) with g(
x
).
correct
incorrect
Convolutions are not commutative: the convolution of f(
x
) with g(
x
) is not the same as that of g(
x
) with f(
x
).
correct
incorrect
The Fourier transform of a product of two functions is the convolution of their Fourier transforms.
correct
incorrect
The Fourier transform of the convolution of two functions is the product of their Fourier transforms.
correct
incorrect
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