Question 1 of 60Fundamentals of Signals & Systems
A signal defined only at discrete instants of time is called a:
AContinuous-time signal
BDiscrete-time signal
CPeriodic signal only
DEnergy signal only
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Question 2 of 60Fundamentals of Signals & Systems
A signal x(t) is periodic if:
Ax(t) = x(t+T) for some T > 0
Bx(t) is always zero
Cx(t) has finite energy only
Dx(t) is causal
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Question 3 of 60Fundamentals of Signals & Systems
An energy signal is characterized by:
AFinite energy and zero average power
BInfinite energy and finite average power
CBoth infinite energy and infinite power
DZero energy always
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Question 4 of 60Fundamentals of Signals & Systems
A signal x(t) is even if:
Ax(−t) = −x(t)
Bx(−t) = x(t)
Cx(t) = 0 for t<0
Dx(t) is periodic
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Question 5 of 60Fundamentals of Signals & Systems
A causal system's output at any time depends on:
AFuture inputs only
BPresent and past inputs only
CPast outputs only
DNothing
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Question 6 of 60Fundamentals of Signals & Systems
The unit impulse function δ(t) has:
AInfinite width and zero area
BZero width (ideally) and unit area
CUnit width and unit area
DNegative area
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Question 7 of 60Fundamentals of Signals & Systems
Time-scaling a signal as x(2t) compared to x(t) results in:
ACompression in time
BExpansion in time
CNo change
DTime reversal only
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Question 8 of 60Fundamentals of Signals & Systems
An LTI system is fully characterized by its:
AInput signal alone
BImpulse response
COutput signal alone
DSampling rate
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Question 9 of 60Fundamentals of Signals & Systems
The output of a continuous-time LTI system is obtained by:
AMultiplying the input and impulse response
BConvolving the input with the impulse response
CAdding the input and impulse response
DDifferentiating the input
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Question 10 of 60Fundamentals of Signals & Systems
Two signals are said to be orthogonal over an interval if:
ATheir sum is zero
BThe integral of their product over that interval is zero
CThey have the same amplitude
DThey are both periodic
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Question 11 of 60Laplace Transforms
The Laplace transform of the unit step function u(t) is:
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Question 12 of 60Laplace Transforms
The Laplace transform of the unit impulse function δ(t) is:
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Question 13 of 60Laplace Transforms
The Laplace transform of e^(−at)u(t) is:
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Question 14 of 60Laplace Transforms
Differentiation in the time domain corresponds, in the Laplace domain, to:
ADividing X(s) by s
BMultiplying by s (and subtracting the initial condition)
CSquaring X(s)
DNo change
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Question 15 of 60Laplace Transforms
Heaviside's expansion theorem is primarily used to:
ASolve nonlinear equations
BFind the coefficients of a partial fraction expansion
CCompute the Fourier transform
DDesign digital filters
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Question 16 of 60Laplace Transforms
The transfer function H(s) of a system is defined as:
AY(s) × X(s)
BY(s)/X(s), assuming zero initial conditions
CX(s)/Y(s)
DThe system's physical mass
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Question 17 of 60Laplace Transforms
The frequency response of a system is obtained from its transfer function H(s) by substituting:
As = 0
Bs = jω
Cs = −1
Ds = ∞
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Question 18 of 60Laplace Transforms
One major advantage of using the Laplace transform to solve differential equations is that it converts them into:
APartial differential equations
BAlgebraic equations
CNonlinear equations
DIntegral equations only
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Question 19 of 60Laplace Transforms
The final value theorem allows determination of:
AThe initial value of x(t) from X(s)
BThe steady-state (final) value of x(t) as t→∞, from X(s)
CThe Fourier transform of x(t)
DThe z-transform of x(t)
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Question 20 of 60Laplace Transforms
The Laplace transform of a ramp function t·u(t) is:
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Question 21 of 60Fourier Series & Transforms
The Fourier series represents a periodic signal as a sum of:
ARandom noise components
BHarmonically related complex exponentials (or sines/cosines)
COnly a single sinusoid
DImpulse functions only
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Question 22 of 60Fourier Series & Transforms
The Fourier transform is primarily used to analyze:
AOnly periodic signals
BAperiodic (and, with impulses, periodic) signals in the frequency domain
COnly discrete-time signals
DOnly DC signals
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Question 23 of 60Fourier Series & Transforms
Parseval's theorem relates:
ATime-domain energy to frequency-domain energy of a signal
BTwo completely unrelated systems
COnly discrete-time signals
DStability margins
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Question 24 of 60Fourier Series & Transforms
The Discrete-Time Fourier Transform (DTFT) of an aperiodic discrete-time signal is:
ADiscrete and aperiodic in frequency
BContinuous and periodic in frequency (with period 2π)
CAlways zero
DIdentical to the z-transform for all z
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Question 25 of 60Fourier Series & Transforms
The Discrete-Time Fourier Series (DTFS) applies to:
AAperiodic discrete-time signals
BPeriodic discrete-time signals, using a FINITE number of harmonics
COnly continuous-time signals
DOnly energy signals
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Question 26 of 60Fourier Series & Transforms
In exponential Fourier series notation, x(t) = Σcₖ e^(jkω0t), the coefficients cₖ are called the:
AImpulse responses
BFourier series coefficients
CPoles of the system
DSampling instants
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Question 27 of 60Fourier Series & Transforms
The fundamental frequency ω0 of a periodic signal with period T is given by:
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Question 28 of 60Fourier Series & Transforms
Convolution in the time domain corresponds, in the Fourier frequency domain, to:
AConvolution again
BMultiplication
CDivision
DDifferentiation
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Question 29 of 60Fourier Series & Transforms
Which of the following signal properties must generally be satisfied (Dirichlet conditions) for a periodic signal to have a valid Fourier series?
AIt must be a pure sinusoid
BIt must satisfy conditions such as absolute integrability over one period
CIt must be discrete-time only
DIt must be causal
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Question 30 of 60Fourier Series & Transforms
Multiplication in the time domain corresponds, in the frequency domain, to:
AMultiplication
BConvolution
CAddition
DSubtraction
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Question 31 of 60Z-Transform & Digital Systems
According to the Nyquist-Shannon sampling theorem, a bandlimited signal can be perfectly reconstructed if the sampling frequency is:
AEqual to the maximum signal frequency
BGreater than twice the maximum signal frequency
CLess than the maximum signal frequency
DZero
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Question 32 of 60Z-Transform & Digital Systems
Aliasing occurs when a signal is sampled:
AAbove the Nyquist rate
BBelow the Nyquist rate
CAt exactly the Nyquist rate only
DUsing an ideal reconstruction filter
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Question 33 of 60Z-Transform & Digital Systems
A Zero-Order Hold (ZOH) reconstructs a continuous signal from samples by:
AInterpolating with a sine function
BHolding each sample value constant until the next sample arrives
CDifferentiating between samples
DDiscarding every other sample
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Question 34 of 60Z-Transform & Digital Systems
The z-transform is defined as:
AX(z) = Σx[n]zⁿ
BX(z) = Σx[n]z⁻ᴸ
CX(z) = ∫x(t)e⁻ᴸᴹdt
DX(z) = x[n]/z
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Question 35 of 60Z-Transform & Digital Systems
The z-transform reduces to the discrete-time Fourier transform (DTFT) when evaluated:
AOn the real axis
BOn the unit circle, z = e^(jω)
CAt z = 0
DAt z = ∞
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Question 36 of 60Z-Transform & Digital Systems
For a discrete-time LTI system to be BIBO stable, all poles of its transfer function H(z) must lie:
AOutside the unit circle
BStrictly inside the unit circle (|z|<1)
CExactly on the unit circle
DAt the origin only
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Question 37 of 60Z-Transform & Digital Systems
The Fast Fourier Transform (FFT) is significant because it:
AComputes the DFT with much lower computational complexity than direct calculation
BReplaces the need for sampling
COnly works for continuous-time signals
DIncreases the required computation to O(N²)
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Question 38 of 60Z-Transform & Digital Systems
The DFT (Discrete Fourier Transform) operates on:
AA continuous, infinite-duration signal
BA finite-length discrete-time signal
COnly analog voltages
DOnly impulse functions
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Question 39 of 60Z-Transform & Digital Systems
Converting a continuous-time signal into a discrete-time signal by taking values at regular intervals is called:
AQuantization
BSampling
CModulation
DFiltering
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Question 40 of 60Z-Transform & Digital Systems
The computational complexity of the FFT algorithm, compared to direct DFT computation, is reduced from O(N²) to approximately:
AO(N)
BO(N log N)
CO(N³)
DO(1)
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Question 41 of 60Applications of Frequency Domain Analysis
Frequency-domain techniques such as Bode and Nyquist plots are primarily used for:
ATime-domain simulation only
BStability analysis of systems
CPhysical construction of circuits
DManufacturing cost estimation
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Question 42 of 60Applications of Frequency Domain Analysis
Spectral analysis is primarily concerned with examining a signal's:
APhysical weight
BFrequency content/spectrum
CColor
DManufacturing origin
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Question 43 of 60Applications of Frequency Domain Analysis
Spectrum sensing (e.g., in cognitive radio) is used to:
ADetect which parts of the frequency spectrum are occupied or free
BIncrease transmitted power indefinitely
CEliminate the need for antennas
DConvert analog signals to digital only
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Question 44 of 60Applications of Frequency Domain Analysis
Autocorrelation measures the similarity between:
ATwo completely different, unrelated signals
BA signal and a time-shifted version of itself
CTwo different systems' transfer functions
DA signal and random noise only
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Question 45 of 60Applications of Frequency Domain Analysis
Cross-correlation is primarily used to measure:
AThe similarity between two different signals
BThe stability margin of a system
CThe sampling rate required
DThe DC gain of a filter
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Question 46 of 60Applications of Frequency Domain Analysis
Frequency-domain system design typically specifies desired behaviour in terms of:
AOnly time-domain overshoot
BBandwidth, gain, phase margin, or cutoff frequency
CPhysical size of components only
DManufacturing tolerances only
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Question 47 of 60Applications of Frequency Domain Analysis
Correlation techniques are especially useful for:
ADetecting signals buried in noise
BIncreasing a system's physical size
CEliminating the need for filters entirely
DRemoving all frequency content
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Question 48 of 60Applications of Frequency Domain Analysis
In frequency-domain stability analysis, gain margin and phase margin are used to indicate:
AHow close a system is to becoming unstable
BThe exact time-domain response
CThe sampling frequency
DThe DC resistance of the circuit
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Question 49 of 60Applications of Frequency Domain Analysis
Spectral analysis using the DFT/FFT helps identify:
ADominant frequency components and harmonics in a signal
BOnly the DC component
CThe physical temperature of a circuit
DNothing useful
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Question 50 of 60Applications of Frequency Domain Analysis
Compared to pure time-domain design, frequency-domain design is often preferred because it:
AIs always less accurate
BProvides a more intuitive way to specify bandwidth, gain and phase requirements
CCannot be used for filter design
DIgnores stability considerations
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Question 51 of 60Filters
An ideal filter is characterized by:
AA gradual roll-off between passband and stopband
BA perfectly sharp (brick-wall) transition between passband and stopband
CInfinite passband ripple
DZero passband gain
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Question 52 of 60Filters
A Butterworth filter is known for having a:
AMaximally flat magnitude response in the passband
BRipple in both passband and stopband
CThe sharpest possible roll-off of all filter types
DNo frequency response at all
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Question 53 of 60Filters
A Chebyshev Type I filter, compared to a Butterworth filter of the same order, typically offers:
AA flatter passband but slower roll-off
BA sharper roll-off but with passband ripple
CNo roll-off at all
DOnly a stopband response
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Question 54 of 60Filters
Passive filters are built using:
AOnly active amplifying elements
BOnly R, L, C components, with no external power
COnly digital logic gates
DOnly operational amplifiers
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Question 55 of 60Filters
An FIR (Finite Impulse Response) digital filter is characterized by:
AAn impulse response of infinite duration
BAn impulse response of finite duration, and inherent stability
CThe need for feedback always
DGuaranteed instability
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Question 56 of 60Filters
An IIR (Infinite Impulse Response) digital filter uses:
ANo feedback at all
BFeedback, giving an impulse response of infinite duration
COnly finite-duration responses
DOnly analog components
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Question 57 of 60Filters
Compared to an IIR filter of similar specification, an FIR filter generally:
ARequires a lower filter order
BRequires a higher filter order, but can have exactly linear phase
CIs always unstable
DCannot be implemented digitally
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Question 58 of 60Filters
A band-stop (notch) filter is designed to:
APass a specific band of frequencies
BReject a specific band of frequencies, passing the rest
CPass only DC
DAmplify all frequencies equally
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Question 59 of 60Filters
The transfer function of a digital filter is typically expressed as a function of:
As, the Laplace variable
Bz, the z-transform variable
COnly time t
DOnly frequency f in Hz
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Question 60 of 60Filters
Active filters, compared to passive filters, have the key advantage of being able to:
AProvide signal gain
BOperate without any power supply
CEliminate all frequency-selective behavior
DFunction only at DC
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