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Test: Signals & Systems - 2 - Question 1

For a given periodic sequence x (n) = {1, 1, 0, 0} with period N = 4, the Fourier coefficient is denoted by c_{k}. The Value of c_{3}* is:

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Test: Signals & Systems - 2 - Question 2

Consider the following difference equation:

y[n] + 3y[n – 1] + 2y[n – 2] = 2x[n] – x[n – 1]

If y[-1] = 0, y[-2] = 1, x[n] = u[n], then y[n] can be represented as

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Test: Signals & Systems - 2 - Question 3

The Fourier series coefficients of a periodic signal x(t), with fundamental frequency and the rest are zero. Suppose x(t) is the input to a band-pass filter with the following magnitude and phase responses.

Let y(t) be the output of the filter and the Fourier series of x(t) in the trigonometric form

x(t) and the steady state response of y(t) are

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Test: Signals & Systems - 2 - Question 4

The discrete Fourier series representation for the following sequence:

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Test: Signals & Systems - 2 - Question 5

For a finite support signal x[n] = r[n] (u[n] – u[n – 11]) where r[n] is the discrete-time ramp function, the energy of x[n] is

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Test: Signals & Systems - 2 - Question 6

The percentage of the total energy dissipated by a 1Ω resistor in the frequency band 0 < ω < 10 rad/s when the voltage across it is v(t) = e^{-2t} u(t) is _________

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Test: Signals & Systems - 2 - Question 7

The z-transform of a sequence x[n] is given as x(z) = 3 + 4z – 6z^{-1} + 2z^{-2}

If y[n] is the first difference of x[n], then y(z) is given by

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Test: Signals & Systems - 2 - Question 9

The DTFT of a signal f(n) = {a, b, c, d} is F(ω). The inverse DTFT of F(ω - π) is:

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Test: Signals & Systems - 2 - Question 11

What is the signal corresponding to the following z-transform? (Where u[n] is the unit-step signal)

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Test: Signals & Systems - 2 - Question 12

Let If y(t) = x(t - 2) then what is value of Y(e^{jω}) at ω = π is ________

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Test: Signals & Systems - 2 - Question 13

The DTFT of x[n] = 0.5n u[n] using geometric series is:

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Test: Signals & Systems - 2 - Question 14

A discrete time signal x[n] and its discrete Fourier transform X(k) related by Another discrete series with Fourier coefficients Y(k) given as Y(k) = X(k - 4) + X(k + 4) then the corresponding sequence y[n] will be

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Test: Signals & Systems - 2 - Question 15

Consider a signal y(t) = x1(t) * x_{2}(t). If x1(t) = 2 cos 4t u(t) and x_{2}(t) = sin 2t u(t). The value of y(t) at t = π / 2 is _______

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Test: Signals & Systems - 2 - Question 17

The sequence x[n] is (0.7)^{n} u(n) and y (n) is x (n)*x (n). Then which of the following statement(s) is/are true?

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Test: Signals & Systems - 2 - Question 18

Consider a system with frequency response of and suppose that the input to the system is x(t) = e-t u(t). If the output response is y(t), the value of y(1) is _______ (answer up to two decimal places)

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Test: Signals & Systems - 2 - Question 19

Let denote the Fourier transform of the signal x[n], where:

The value of at n = 0 will be ________. (The arrow represents the origin)

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Test: Signals & Systems - 2 - Question 20

Which of the following systems are linear time-invariant and causal systems.

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