Q. Which of the following represents a stable system?

1. Impulse response decreases exponentially.
2. Area within the impulse response in finite.
3. Eigen values of the system are positive and real.
4. Roots of the characteristic equation of the system are real and positive.

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Q. Auto correlation for τ = 0 is equal to

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Q. X and Y are two random variable and Z = X + Y. Let σ²x, σ²y and σ²z be variance of X, Y and Z. Then

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Q. Assertion (A): The conditions under which it is possible to write Fourier series of a periodic function are called Drichlet conditions.

Reason (R): If f(t) = - f(- t), it is refereed to as odd symmetry.

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Q. L[c1f1(t) + c2f2(t)] =

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Q. If a linear time invartant system is exicited by a pure random signal like white noise, the output of the linear system will have which of the following properties?

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Q. A signum function is

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Q. FIR filter Passes __________ Phase.

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Q. A trigonometric series has

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Q. If a number of odd functions are added, the resultant sum is

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Q. In what range should Re(s) remains so that Laplace transform of the function e^[(a + 2)t + 5] exists?

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Q. Which one of the following rules determines the mapping of s-plane to z-plane?

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Q. For the signum function sgn(t), F(jω) =

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Q. If a sequence is causal then ROC is (where a is any number)

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Q. If f1(t)<< F1(jω) and f2(t)↔ F2(jω), then [a1 f1(t) + a2f2(t)]↔

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Q. The signal x(t) = A cos (ω₀t + φ) is

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Q. The inverse Fourier transform of δ(t) is

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Q. Which one of the following is the correct statement of the system characterized by the equation y(t) = ax(t) + b?

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Q. The derivative of unit step function is

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Q. The coefficients Fn in the exponential form of Fourier series are

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