Signals & Systems interview questions

1. A.the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane
2. B.energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy
3. C.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
4. D.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation

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1. A.Energy and power signals
2. B.Nyquist rate
3. C.Group delay
4. D.Paley-Wiener criterion

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1. A.Energy and power signals — a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters
2. B.Energy and power signals — minimum sampling frequency, twice the highest frequency in a band-limited signal, below which spectral copies overlap and aliasing occurs
3. C.Energy and power signals — set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
4. D.Energy and power signals — energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy

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1. A.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
2. B.set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
3. C.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
4. D.a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters

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1. A.Z-transform region of convergence
2. B.Unit impulse function
3. C.Paley-Wiener criterion
4. D.Energy and power signals

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1. A.Unit impulse function — if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
2. B.Unit impulse function — a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters
3. C.Unit impulse function — generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
4. D.Unit impulse function — energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy

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1. A.minimum sampling frequency, twice the highest frequency in a band-limited signal, below which spectral copies overlap and aliasing occurs
2. B.a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters
3. C.the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane
4. D.energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy

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1. A.Final value theorem
2. B.Nyquist rate
3. C.Hilbert transform
4. D.Paley-Wiener criterion

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1. A.Nyquist rate — operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
2. B.Nyquist rate — generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
3. C.Nyquist rate — negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
4. D.Nyquist rate — minimum sampling frequency, twice the highest frequency in a band-limited signal, below which spectral copies overlap and aliasing occurs

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1. A.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
2. B.if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
3. C.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
4. D.set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle

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1. A.Energy and power signals
2. B.Nyquist rate
3. C.Group delay
4. D.Duality of Fourier transform

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1. A.Duality of Fourier transform — negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
2. B.Duality of Fourier transform — the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane
3. C.Duality of Fourier transform — generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
4. D.Duality of Fourier transform — if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions

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1. A.energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy
2. B.set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
3. C.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
4. D.the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane

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1. A.Final value theorem
2. B.Paley-Wiener criterion
3. C.Z-transform region of convergence
4. D.Nyquist rate

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1. A.Final value theorem — if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
2. B.Final value theorem — operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
3. C.Final value theorem — negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
4. D.Final value theorem — the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane

Answer + AI explanation with Pro

1. A.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
2. B.if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
3. C.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
4. D.negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion

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1. A.Paley-Wiener criterion
2. B.Hilbert transform
3. C.Duality of Fourier transform
4. D.Group delay

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1. A.Group delay — operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
2. B.Group delay — if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
3. C.Group delay — minimum sampling frequency, twice the highest frequency in a band-limited signal, below which spectral copies overlap and aliasing occurs
4. D.Group delay — negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion

Answer + AI explanation with Pro

1. A.generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
2. B.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
3. C.set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
4. D.the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane

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1. A.Hilbert transform
2. B.Energy and power signals
3. C.Nyquist rate
4. D.Z-transform region of convergence

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1. A.Hilbert transform — the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane
2. B.Hilbert transform — energy signals have finite total energy and zero average power, whereas power signals such as periodic waveforms have finite non-zero average power and infinite energy
3. C.Hilbert transform — operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
4. D.Hilbert transform — a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters

Answer + AI explanation with Pro

1. A.a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters
2. B.if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions
3. C.negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
4. D.operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation

Answer + AI explanation with Pro

1. A.Z-transform region of convergence
2. B.Group delay
3. C.Final value theorem
4. D.Paley-Wiener criterion

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1. A.Paley-Wiener criterion — generalised function that is zero except at the origin with unit area, whose sifting property picks out the value of any signal at the instant where it is located
2. B.Paley-Wiener criterion — set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
3. C.Paley-Wiener criterion — a magnitude response can belong to a causal system only if the integral of |ln|H(ω)||/(1 + ω²) is finite, which rules out ideal brick-wall filters
4. D.Paley-Wiener criterion — if x(t) transforms to X(f) then X(t) transforms to x(−f), which is why a rectangular pulse and a sinc function are transforms of each other in both directions

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1. A.minimum sampling frequency, twice the highest frequency in a band-limited signal, below which spectral copies overlap and aliasing occurs
2. B.the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane
3. C.negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
4. D.set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle

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1. A.Duality of Fourier transform
2. B.Z-transform region of convergence
3. C.Hilbert transform
4. D.Energy and power signals

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1. A.Z-transform region of convergence — negative derivative of phase response with respect to frequency, constant for linear-phase systems so that all frequency components are delayed equally without waveform distortion
2. B.Z-transform region of convergence — set of z where the transform sum converges; a causal sequence has the exterior of a circle, and the system is stable only when it includes the unit circle
3. C.Z-transform region of convergence — operation that shifts every frequency component by −90° while leaving magnitudes unchanged, used to build the analytic signal and single-sideband modulation
4. D.Z-transform region of convergence — the steady-state value of f(t) equals the limit of sF(s) as s approaches zero, valid only when all poles of sF(s) lie in the left half-plane

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