Signals and Systems
Z Transform
Practice questions from Z Transform.
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IncorrectConsider the infinite-length, discrete-time sequence , where is an integer. The region of convergence of its Z-transform is given by: (Note: is a complex variable)
such that such that
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Sign in to UnlockIf the -transform of a finite-duration discrete-time signal is , then the transform of the signal is
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Sign in to UnlockThe Z-transform of a discrete signal is
Which one of the following statements is true?
Discrete-time Fourier transform of converges if is
Discrete-time Fourier transform of converges if is
Discrete-time Fourier transform of converges if is such that is a left-sided sequence
Discrete-time Fourier transform of converges if is such that is a rightsided sequence
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Sign in to UnlockThe causal signal with z-transform is (u[n] is the unit step signal)
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Sign in to UnlockConsider a signal , where u[n] = 0 if n < 0, and u[n] = 1 if n ≥ 0. The z-transform x[n – k], k > 0 is with region of convergence being
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Sign in to UnlockThe pole-zero plots of three discrete-times systems P, Q and R on the z-plane are shown below.
Which one of the following is TRUE about the frequency selectivity of these systems?
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Sign in to UnlockConsider a discrete time signal given by
The region of convergence of its Z – transform would be
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Sign in to UnlockLet be the Z – transform of a causal signal x[n], Then, the values of x[2] and x[3] are
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Sign in to UnlockIf , then the region of convergence (ROC) of its Z-transform in the Z-plane will be
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Sign in to UnlockThe z-transform of a signal x[n] is given by. It is applied to a system, with a transfer function. Let the output be y(n). Which of the following is true?
y(n) is non casual with finite support
y(n) is casual with infinite support
;;
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Sign in to UnlockH(z) is a transfer function of a real system. When a signal is the input to such a system, the output is zero. Further the Region of Convergence (ROC) of is the entire Z-plane (except z = 0). It can then be inferred that H(z) can have a minimum of
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Sign in to UnlockGiven with , the residue of at for will be
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Sign in to UnlockConsider the discrete-time system shown in the figure where the impulse response of G(z) is g(0) = 0, g(1) = g(2) = 1, g(3) = g(4) = ……. = 0
This system is stable for range of values of K
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Sign in to Unlock, are Z-transforms of two signals x[n], y[n] respectively. A linear time invariant system has the impulse response h[n] defined by these two signals as , where * denotes discrete time convolution. Then the output of the system for the input
Has Z-transform
Has Z-transform
Does not satisfy any of the above three.
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Sign in to UnlockA signal is processed by a causal filter with transfer function G(s). For a distortion free output signal waveform, G(s) must
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Sign in to Unlockis a low-pass digital filter with a phase characteristics same as that of the above question if
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Sign in to UnlockThe discrete time signal , where ↔ denotes a transform-pair relationship, is orthogonal to the signal.
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Sign in to Unlocky[n] denotes the output and x[n] denotes the input of a discrete-time system given by the difference equation y[n] – 0.8y[n – 1] = x[n] + 1.25x[n + 1]. Its right-sided impulse response is
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Sign in to UnlockA discrete real all pass system has a pole at : it, therefore
also has a pole at
has a constant phase response over the -plane:
is stable only if it is anti-causal
has a constant phase response over the unit circle:
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Sign in to UnlockIf u(t) is the unit step and δ(t) is the unit impulse function, the inverse z-transform of for k ≥ 0 is:
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