Difficulty: Easy & Basic
Hertz measures which signal property?
A Energy
B Time delay
C Frequency
D Amplitude
Answer: C. Frequency Frequency counts cycles per second and is measured in hertz.
The average of a periodic signal over one period is called what?
A DC component
B Time constant
C Impulse response
D Nyquist rate
Answer: A. DC component The mean over a fundamental period is the signal’s DC component.
Subtracting the time-reversed signal isolates what component?
A Even component
B DC component
C Impulse component
D Odd component
Answer: D. Odd component The odd component is [x(t)−x(−t)]/2.
When u(t) drives an LTI system, which response is observed?
A Frequency response
B Step response
C Natural response
D Impulse response
Answer: B. Step response The step response is the output to a unit-step input.
In the frequency domain, time convolution becomes which operation?
A Differentiation
B Sampling
C Multiplication
D Time reversal
Answer: C. Multiplication The Fourier transform of a convolution is the product of the transforms.
Cascade impulse responses combine through what operation?
A Sample them
B Convolve them
C Add them always
D Differentiate them
Answer: B. Convolve them The cascade’s overall impulse response is the convolution of the individual responses.
For input eʲωᵗ, how does an LTI system shape the output?
A Amplitude and phase
B Frequency and period
C Time and index
D Energy and power
Answer: A. Amplitude and phase A sinusoid passes through an LTI system at the same frequency, with amplitude and phase set by H(jω).
Given a real impulse response h(t), what symmetry links H(jω) and H(−jω)?
A H(jω)=−H*(jω)
B H(jω)=1
C H(−jω)=H(jω)
D H(−jω)=H*(jω)
Answer: D. H(−jω)=H*(jω) The Fourier transform of a real signal has conjugate symmetry across zero frequency.
Replacing x(t) by x(t+τ), τ>0, causes which shift?
A Advance
B Delay
C Amplitude scaling
D Time reversal
Answer: A. Advance Adding a positive value inside the argument shifts the waveform to the left.
Differentiating the step response yields what for a CT LTI system?
A h(t)=s(t+1)
B h(t)=∫s(t)dt
C h(t)=ds(t)/dt
D h(t)=s(t)²
Answer: C. h(t)=ds(t)/dt Differentiating the unit-step response gives the impulse response for an LTI system.
Causality forces h(t) to be what for t<0?
A A constant
B 0
C δ(t)
D 1
Answer: B. 0 A causal impulse response is zero before the impulse is applied.
For CT LTI BIBO stability, which integral must be finite?
A ∫h(t)dt is zero
B h(t) is periodic
C h(t) is nonzero
D ∫|h(t)|dt is finite
Answer: D. ∫|h(t)|dt is finite Absolute integrability of h(t) is the BIBO stability condition for a continuous-time LTI system.
At time t, what input value may a memoryless system use?
A Future input only
B Past input only
C Current input only
D All future samples
Answer: C. Current input only A memoryless output depends only on the input at the same instant.
The impulse response h[n]=δ[n]+δ[n−1] contains how many nonzero taps?
A Two taps
B Three taps
C No taps
D One tap
Answer: A. Two taps It has nonzero samples at n=0 and n=1, so it is a two-tap FIR response.
Discrete-time LTI convolution sums which terms?
A Integral over time
B Sum over shifted products
C Derivative of input
D Product at each index
Answer: B. Sum over shifted products The convolution sum adds x[k]h[n−k] across all integer k.
Changing φ in cos(Ω₀n+φ) alters which parameter directly?
A Amplitude
B Frequency
C Sampling rate
D Phase
Answer: D. Phase Changing φ changes the sinusoid’s phase offset.
Undersampling makes different signal frequencies indistinguishable; what is this effect?
A Oversampling
B Time reversal
C Aliasing
D Clipping
Answer: C. Aliasing Aliasing makes distinct frequencies produce the same sampled sequence.
For a bandlimited signal ending at fmax, its Nyquist rate is what?
A 4fmax
B 2fmax
C fmax/2
D fmax
Answer: B. 2fmax The Nyquist rate is twice the highest frequency present in a bandlimited signal.
DTFT repeats after which increment in Ω?
A 2π
B π
C 1
D It is aperiodic
Answer: A. 2π The DTFT repeats every 2π radians per sample.
Bilateral Laplace transforms use which complex variable?
A Real time t only
B Angular frequency Ω only
C Integer n
D Complex s
Answer: D. Complex s The Laplace transform uses the complex variable s=σ+jω.
With zero external input but nonzero stored energy, which response remains?
A Zero-state response
B Zero-input response
C Impulse response
D Step response
Answer: B. Zero-input response Stored initial conditions can produce a response even when the external input is zero.
Z-transform analysis uses which complex variable?
A Continuous t
B Complex s only
C Complex z
D Real amplitude only
Answer: C. Complex z The Z-transform uses a complex variable z.
The factor u[n] makes aⁿu[n] what type of sequence?
A Periodic
B Two-sided only
C Left-sided
D Right-sided
Answer: D. Right-sided The unit step makes the sequence zero for n<0, so it is right-sided.
If x(t)=δ(t−τ), what output does an LTI system produce?
A h(t−τ)
B δ(t−τ)
C h(t+τ)
D τh(t)
Answer: A. h(t−τ) Time invariance shifts the impulse response by the same τ as the delayed impulse input.
Multiplication by δ[n−k] retains which sample of x[n]?
A Every sample of x[n]
B Only x[0]
C No sample
D Sample x[k] at k
Answer: D. Sample x[k] at k Multiplying by the shifted unit sample keeps only the value at n=k.