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Value of b_{n} for the periodic function f with period 2π defined as follows :
Select one:
The function is bounded, integrable and piece wise monotonic on
Let us determine the Fourier coefficients
The correct answer is:  1/n, for n even
For the given periodic function The coefficient b_{1} of the continuous Fourier series associated with the given function f(t) can be computed as
Select one:
The coefficient b_{1} of the continuous Fourier series associated with the above given function f(t) can be computed as
since and
Hence
b_{1} = –0.7468
The correct answer is: –0.7468
Given the following periodic function, f(t).
f (t) = { t^{2} for 0 ≤ t ≤ 2 ; t + 6 for 2 ≤ t ≤ 6
The coefficient a_{0} of the continuous Fourier series associated with the above given function f(t) can be computed as
Select one:
The coefficient a_{0} of the continuous Fourier series associated with the given function f(t) can be computed as
The correct answer is: 16/9
For the given periodic function with a period T = 6. The Fourier coefficient a_{1} can be computed as
Select one:
The coefficient a_{1} of the continuous Fourier series associated with the above given function f(t) can be computed with k = 1 and T = 6 as following :
a_{1} = –0.9119
The correct answer is: –0.9119
Sum of the series at for the periodic function f with period 2π is defined as
Select one:
The function is piece wise monotonic, bounded and integrable on [π, π] Let us compute its Fourier coefficients
The function is continuous at all points of [π, π] except
which holds at all points with the exception of all discontinuities,
At the sum of the series
The correct answer is: 0
Which of the following is an “even” function of t?
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Since if we replace “t” by “–t”, then the function value remains the same!
The correct answer is: t^{2}
A “periodic function” is given by a function which
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Since the function’s value remains the same value after a period (or multiple periods) has passed!
The correct answer is: satisfies f(t + T) = f(t)
For the given periodic function with a period T = 6. The complex form of the Fourier series can be expressed as The complex coefficient can be expressed as
Select one:
The coefficient (corresponding to k = 1) can be expressed as :
The coefficient b_{1} of the continuous Fourier series associated with the above given function f(t) can be computed as
since
and
Hence
b_{1} = –0.7468
The coefficient a_{1} of the continuous Fourier series associated with the above given function f(t) can be computed with k = 1 and T = 6 as following :
a_{1} = –0.9119
The correct answer is: –0.4560 + 0.3734i
The function x^{2} is periodic with period 2l on the interval [–l, l]. The value of a_{n} is given by
Select one:
The substitution transforms the function into a periodic function with period . Moreover it is an even function.
∴ b_{n} = 0, n = 1, 2, 3,.....
The correct answer is: for n even
The function x^{2} extended as an odd function in [–l, l] by redefining it as
sum of series at x = l.
Select one:
Substitution of transforms it into an odd periodic function on [π, π],
so that the Fourier coefficients are
a_{n} = 0 for n = 0, 1, 2, 3
At x = 0, a point of continuity of the function, the sum of the series is zero, a fact which may be verified directly from series.
At x = l, the sum of series =
The correct answer is: 0
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