A system is defined by its impulse response h(n) = 2n u(n - 2). The system is
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A discrete time linear shift-invariant system has an impulse response h[n] with h[0] = 1, h[1] = -1, h[2] = 2, and zero otherwise. The system is given an input sequence x[n] with x[0] = x[2] = 1 and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively
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If the impulse response of a discrete-time system is h[n] = -5nu[- n - 1], then the system function H(z) is equal to
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For an N-point FFT algorithm with N = 2m, which one of the following statements is TRUE?
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A discrete-time signal x [n] = sin(π2 n), n being an integer, is
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Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems (u(t) denotes the unit-step function)?
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The Fourier Transform of a function x(t) is X(f). The Fourier transform of will be
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The magnitude and phase of the complex Fourier series coefficient ak of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
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Let the signal i(t) = 0 outside the interval [T1, T2], where T1 and T2 are finite. Furthermore, |f(t)| < ∞. The region of convergence (ROC) of the signal's bilateral Laplace transform F(s) is
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The z-transform F(z) of the function f(nT) = anT is
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The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,
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For the discrete-time system shown in the figure, the poles of the system transfer function are located at
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Let
The Region of Convergence (ROC) of the z-transform of x[n]
The Region of Convergence (ROC) of the z-transform of x[n]
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An LTI system having transfer function and input x(t) = sin(t + 1) is in steady state. The output is sampled at a rate ωs rad/s to obtain the final output {y(k)}. Which of the following is true?
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Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z).
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If G(f) represents the Fourier transform of a signal g(t) which is real and odd symmetric in time, then
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Consider the sequence
x[n] = {-4 - j5, 1 + j2, 4}
The conjugate antisymmetric part of the sequence is
x[n] = {-4 - j5, 1 + j2, 4}
The conjugate antisymmetric part of the sequence is
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If the region of convergence of x1[n] + x2[n] is then the region of convergence of x1[n] - x2[n] includes
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The Fourier series of an odd periodic function, contains only
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Increased pulse-width in the flat-top sampling, leads to
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