Difficulty: Easy & Basic
For an ideal band-limited signal, which sampling rate meets Nyquist?
A Below twice fmax
B At least twice fmax
C Exactly its bandwidth
D Any positive rate
Answer: B. At least twice fmax. The sampling theorem requires a rate at least twice the highest signal frequency for ideal reconstruction.
Discrete-time samples are indexed by which values?
A Continuous time values
B Arbitrary real indices
C Only positive seconds
D Integer n values
Answer: D. Integer n values. A discrete-time sequence is indexed at integer instants n.
Quantization makes which signal property discrete?
A Amplitude values
B Sample locations
C Signal duration
D Frequency axis
Answer: A. Amplitude values. Quantization maps each sampled amplitude to one of a finite set of levels.
Before an ADC, which filter helps prevent aliasing?
A Digital high-pass filter
B Post-ADC notch filter
C Analog low-pass filter
D Output reconstruction filter
Answer: C. Analog low-pass filter. An analog anti-alias filter attenuates frequencies above the allowed input band before sampling.
Undersampling can make distinct frequencies appear as what?
A Orthogonal phases
B Quantized levels
C Aliased frequencies
D Impulse responses
Answer: C. Aliased frequencies. Aliasing folds out-of-band components into frequencies that cannot be distinguished from the sampled data.
Given sample rate fs, what is the Nyquist frequency?
A 2 fs
B fs divided by two
C fs divided by four
D fs alone
Answer: B. fs divided by two. The Nyquist frequency is half the sampling rate.
How many levels does an ideal B-bit ADC provide?
A B squared
B 2 times B
C B plus one
D 2 to the B
Answer: D. 2 to the B. B bits encode 2^B distinct code words and hence 2^B quantization levels.
With rounding step Δ, what bounds ideal quantization error?
A Plus or minus Δ/2
B Plus or minus Δ
C Zero to Δ
D Plus or minus 2Δ
Answer: A. Plus or minus Δ/2. Rounding error is bounded by half a quantization step in either direction.
During ADC conversion, which operation creates a bit pattern?
A Sampling
B Reconstruction
C Analog filtering
D Binary encoding
Answer: D. Binary encoding. After sampling and quantization, the converter encodes each level as a binary code.
Between samples, what does a zero-order hold do?
A Draws a straight ramp
B Keeps output constant
C Adds random noise
D Removes every sample
Answer: B. Keeps output constant. A zero-order hold keeps the latest sample value until the next update.
Identify the discrete-time unit impulse.
A δ[n]
B u[n]
C n u[n]
D δ[n−1]
Answer: A. δ[n]. The unit impulse equals one at n=0 and zero at all other integer indices.
Where does δ[n−4] equal one?
A At n equals zero
B At n equals minus four
C At n equals four
D At every index
Answer: C. At n equals four. The shift places the unit impulse at n=4.
Superposition is the defining property of which system class?
A Time-varying systems
B Linear systems
C Noncausal systems
D Periodic systems
Answer: B. Linear systems. A linear system preserves scaled sums of its inputs.
Through causality, which inputs may affect the current output?
A Future inputs only
B Future and present
C All future samples
D Present and past
Answer: D. Present and past. A causal system cannot respond to input values that have not occurred yet.
Which system has a finite-duration impulse response?
A IIR system
B Adaptive system
C FIR system
D State-space model
Answer: C. FIR system. An FIR system’s impulse response has finite duration.
In discrete time, normalized frequency is measured in what?
A Radians per sample
B Seconds per hertz
C Volts per sample
D Samples per second
Answer: A. Radians per sample. Digital angular frequency is commonly expressed in radians per sample.
Unlike the DFT, which transform uses a continuous frequency variable?
A DTFT
B DCT
C FFT
D Z-transform
Answer: A. DTFT. The DTFT represents a discrete-time sequence over a continuous angular-frequency variable.
With N input samples, how many DFT coefficients result?
A N plus one
B 2N coefficients
C N coefficients
D log2 N coefficients
Answer: C. N coefficients. An N-point DFT produces N frequency-domain values.
Low-pass filtering mainly preserves what?
A Above-cutoff frequencies
B Only DC impulses
C All stopband energy
D Below-cutoff frequencies
Answer: D. Below-cutoff frequencies. A low-pass filter passes frequencies below its cutoff and attenuates higher frequencies.
Band-pass filtering selects what?
A Only zero frequency
B A frequency interval
C All high frequencies
D A single time sample
Answer: B. A frequency interval. A band-pass response passes a chosen range of frequencies.
Narrowband rejection is the role of which response?
A Notch filter
B Low-pass filter
C Band-pass filter
D All-pass filter
Answer: A. Notch filter. A notch filter strongly attenuates a narrow frequency band.
At f0=fs/8, what is normalized angular frequency?
A π/8 radians per sample
B π/2 radians per sample
C π/4 radians per sample
D 2π radians per sample
Answer: C. π/4 radians per sample. Normalized angular frequency is 2πf0/fs; substituting f0=fs/8 gives π/4 radians per sample.
At the high-frequency end, which filter passes energy preferentially?
A Low-pass filter
B High-pass filter
C Band-stop filter
D Smoothing filter
Answer: B. High-pass filter. A high-pass filter passes frequencies above its cutoff.
Write the output of a one-sample delay.
A x[n plus one]
B x[2n]
C x[n] plus one
D x[n minus one]
Answer: D. x[n minus one]. A one-sample delay shifts the sequence right: y[n]=x[n−1].
How is the unit step defined for n below zero?
A It equals one
B It equals n
C It equals zero
D It is undefined
Answer: C. It equals zero. For the standard discrete-time unit step, u[n]=0 when n<0.