How does a continuous-time signal differ from a discrete-time signal?
A Defined after sampling
B Defined for every time
C Defined at integer times
D Defined at peaks only
Answer: B. Defined for every time A continuous-time signal is specified for every time value; a discrete-time signal is specified at separate instants.
Replacing t with t−τ, where τ>0, causes which shift?
A Advance
B Time reversal
C Amplitude scaling
D Delay
Answer: D. Delay Subtracting a positive delay from the time argument shifts the waveform to the right.
Given the sinusoid cos(2πf₀t), what is its period?
A 1/f₀
B 2πf₀
C 1/(2πf₀)
D f₀
Answer: A. 1/f₀ A sinusoid completes one cycle in T₀=1/f₀ seconds.
Signals with finite energy and zero average power are classified as what?
A Power signal
B Random signal
C Energy signal
D Periodic signal
Answer: C. Energy signal An energy signal has finite total energy and zero long-term average power.
Persistent nonzero constants belong to which signal class?
A Power signal
B Impulse signal
C Energy signal
D Finite-duration signal
Answer: A. Power signal A nonzero constant over infinite time has infinite energy but finite nonzero average power.
When t>0, what value does the unit step u(t) take?
A Undefined
B −1
C 1
D 0
Answer: C. 1 The unit step equals one for positive time.
The unit impulse δ(t) has what total area?
A Infinite
B 1
C 0
D −1
Answer: B. 1 The ideal unit impulse has unit area, though its width is zero.
LTI abbreviates which system property?
A Low-threshold input
B Linear transfer integration
C Limited-time interpolation
D Linear time-invariant
Answer: D. Linear time-invariant LTI abbreviates linear and time-invariant.
Linearity requires which two forms of superposition?
A Causality and stability
B Energy and power
C Additivity and scaling
D Delay and reversal
Answer: C. Additivity and scaling Linearity requires additivity and homogeneity, also called scaling.
Time invariance requires what input-output relation?
A Output shifts equally
B Input remains unchanged
C Gain varies with time
D Output always vanishes
Answer: A. Output shifts equally For a time-invariant system, shifting the input by τ shifts the output by the same τ.
A system that never uses future input values is called what?
A Time-invariant system
B Memoryless system
C Unstable system
D Causal system
Answer: D. Causal system Causality means the output at a time cannot depend on future input values.
BIBO stability guarantees what for bounded inputs?
A Finite input, finite memory
B Bounded input, bounded output
C Zero input, zero output
D Periodic input, periodic output
Answer: B. Bounded input, bounded output A bounded input must produce a bounded output for a BIBO-stable system.
Frequency response of an LTI system is obtained from h(t) using which transform?
A Time reversal
B Laplace inverse only
C Fourier transform
D Z transform
Answer: C. Fourier transform The frequency response is the Fourier transform of the impulse response.
For an LTI system, combining input with impulse response uses which operation?
A Correlation
B Sampling
C Differentiation
D Convolution
Answer: D. Convolution An LTI output is the convolution of its input with the impulse response.
By definition, which input produces h(t) as the output?
A Unit impulse δ(t)
B Ramp input r(t)
C Unit step u(t)
D Sinusoidal input
Answer: A. Unit impulse δ(t) The impulse response is defined as the output to a unit impulse.
If h(t)=δ(t), how does the system affect x(t)?
A Differentiates x(t)
B Leaves x(t) unchanged
C Reverses x(t)
D Delays x(t)
Answer: B. Leaves x(t) unchanged Convolution with δ(t) reproduces the input exactly.
With ω₀=4π rad/s, what is the period of sin(ω₀t)?
A 2 s
B 0.25 s
C 1 s
D 0.5 s
Answer: D. 0.5 s Here ω₀=4π rad/s, so f₀=2 Hz and T₀=0.5 s.
Angular frequency is measured in which standard unit?
A Radians per second
B Hertz
C Seconds per radian
D Radians per cycle
Answer: A. Radians per second Angular frequency uses radians per second; ordinary frequency uses cycles per second, or hertz.
Periodic continuous-time signals use which harmonic representation?
A Z transform
B Laplace inverse
C Fourier series
D Fourier transform
Answer: C. Fourier series Fourier series represents periodic signals as sums of harmonically related components.
Continuous frequency components of a nonperiodic signal are represented by what transform?
A Fourier series only
B Fourier transform
C Unit-step transform
D Z transform only
Answer: B. Fourier transform The Fourier transform maps a time-domain signal into a continuous frequency-domain representation.
Discrete-time sequences use which standard index?
A Integer n
B Complex s
C Continuous t
D Frequency f only
Answer: A. Integer n A discrete-time sequence is commonly indexed by integers n.
At which index is δ[n] nonzero?
A No index
B Every index
C n=1
D n=0
Answer: D. n=0 The unit sample equals one at n=0 and zero elsewhere.
Reflecting x[n] around n=0 performs what operation?
A Frequency scaling
B Time reversal
C Time delay
D Amplitude shift
Answer: B. Time reversal Replacing n with −n reflects the sequence about n=0.
Period N in discrete time requires which equality for every n?
A x[n+1]=0
B x[N]=n
C x[n+N]=x[n]
D x[n−N]=0
Answer: C. x[n+N]=x[n] A period N is a positive integer shift that leaves every sequence value unchanged.
Even symmetry requires which relation?
A x(t+T)=0
B x(t)=δ(t)
C x(−t)=−x(t)
D x(−t)=x(t)
Answer: D. x(−t)=x(t) An even signal is unchanged by time reversal.