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The Fourier series coefficients of signal x(t) shown in Figure (A) are given as:
c0 = 1/π, c1 = −j/4, cn = 1/π(1 − n2), for k even.
Which of the following Fourier series coefficients of y(t) shown in Figure (B) is/are correct?
c0 = 1/π, c1 = −j/4, cn = 1/π(1 − n2), for k even.
Which of the following Fourier series coefficients of y(t) shown in Figure (B) is/are correct?
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The Fourier series coefficients of signal x(t) shown in Figure (A) are...
Concept:
Time shifting property of Fourier series states that:
Since ω0 = 2π/T0, the above expression can be written as:
Application:
Observing the two figures, we can write:
y(t) = x(t - 1)
Where cn = Fourier series coefficient of x(t)
Since, T0 = 2
Using the above expression, we get:
Also for even values of n, e-jπn = 1
Time shifting property of Fourier series states that:
Since ω0 = 2π/T0, the above expression can be written as:
Application:
Observing the two figures, we can write:
y(t) = x(t - 1)
Where cn = Fourier series coefficient of x(t)
Since, T0 = 2
Using the above expression, we get:
Also for even values of n, e-jπn = 1
Most Upvoted Answer
The Fourier series coefficients of signal x(t) shown in Figure (A) are...
Concept:
Time shifting property of Fourier series states that:
Since ω0 = 2π/T0, the above expression can be written as:
Application:
Observing the two figures, we can write:
y(t) = x(t - 1)
Where cn = Fourier series coefficient of x(t)
Since, T0 = 2
Using the above expression, we get:
Also for even values of n, e-jπn = 1
Time shifting property of Fourier series states that:
Since ω0 = 2π/T0, the above expression can be written as:
Application:
Observing the two figures, we can write:
y(t) = x(t - 1)
Where cn = Fourier series coefficient of x(t)
Since, T0 = 2
Using the above expression, we get:
Also for even values of n, e-jπn = 1
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