Difficulty: Medium
Suppose a 5 kHz tone is sampled at 12 kHz. What happens ideally?
A No aliasing occurs
B It aliases to 1 kHz
C It aliases to 5 kHz
D It becomes DC
Answer: A. No aliasing occurs. The Nyquist frequency is 6 kHz, above the 5 kHz tone, so ideal sampling avoids aliasing.
For 31 taps, what is the delay of a symmetric linear-phase FIR?
A 14 samples
B 16 samples
C 15 samples
D 31 samples
Answer: C. 15 samples. A symmetric N-tap linear-phase FIR has delay (N−1)/2; for N=31 this is 15 samples.
Windowed FIR design begins with which ideal-domain object?
A Digital pole table
B Ideal impulse response
C Random coefficient set
D Quantized spectrum
Answer: B. Ideal impulse response. The window method truncates an ideal infinite-duration impulse response to form a finite FIR.
Stability for a causal IIR requires what pole condition?
A One pole at infinity
B All zeros inside circle
C Poles outside circle
D All poles inside unit circle
Answer: D. All poles inside unit circle. A causal discrete-time rational system is BIBO stable when all poles lie inside the unit circle.
Sinusoidal inputs to an LTI system retain what property?
A Input phase only
B Input amplitude only
C Input sampling rate
D Input frequency
Answer: D. Input frequency. A sinusoid is an eigenfunction of an LTI system, so the output has the same frequency with changed amplitude and phase.
Three equal moving-average taps have zeros at which angles?
A Plus or minus 2π/3
B Zero radians only
C Plus or minus π/3
D Plus or minus π
Answer: A. Plus or minus 2π/3. The numerator 1+z⁻¹+z⁻² vanishes at the two non-DC cube roots of unity.
Before decimation by four, what normalized cutoff avoids aliasing ideally?
A At most π/2
B At most π
C At most π/4
D At most 2π
Answer: C. At most π/4. Downsampling by M reduces the Nyquist limit to π/M, so M=4 requires a cutoff no greater than π/4.
Converting 48 kHz audio to 32 kHz uses which rate ratio L/M?
A 3 over 2
B 2 over 3
C 4 over 3
D 1 over 2
Answer: B. 2 over 3. The output-to-input rate ratio is 32/48=2/3, implemented by interpolation by 2 and decimation by 3.
Threefold interpolation inserts how many zeros between input samples?
A One zero
B Three zeros
C Four zeros
D Two zeros
Answer: D. Two zeros. Upsampling by L inserts L−1 zeros between successive samples; for L=3, that is two.
Canonical direct-form II reduces delay count by sharing what?
A Delay elements
B Input samples
C Output ports
D Frequency bins
Answer: A. Delay elements. Direct-form II shares delay elements between the feedforward and feedback sections.
Butterworth magnitude response is maximally flat where?
A Stopband
B Transition band
C Passband
D Unit circle only
Answer: C. Passband. The Butterworth design has a maximally flat magnitude response in the passband.
Chebyshev type I allows ripple in which band?
A Stopband
B Passband
C Both bands
D Neither band
Answer: B. Passband. Chebyshev type I filters have passband ripple and a monotonic stopband.
Chebyshev type II places ripple in which band?
A Stopband
B Passband
C Both bands
D Neither band
Answer: A. Stopband. Chebyshev type II filters have a monotonic passband and stopband ripple.
Increasing a window-designed FIR length generally narrows what?
A Passband gain
B Sampling interval
C Quantization step
D Transition band
Answer: D. Transition band. More taps generally allow a narrower transition band for a window-designed FIR.
Cascaded LTI blocks combine by which transfer-function operation?
A Addition
B Correlation
C Multiplication
D Time reversal
Answer: C. Multiplication. Transfer functions of cascaded LTI systems multiply.
Hardware MAC units repeatedly perform which operation?
A Division then rounding
B Product plus sum
C Sampling then encoding
D Shift then compare
Answer: B. Product plus sum. A MAC multiplies operands and accumulates their products into a running sum.
For a stable low-pass with unit DC gain, a unit step settles to what?
A Zero
B Its pole radius
C Its sample rate
D One
Answer: D. One. A stable filter with unity DC gain settles to one for a unit-step input.
The difference equation y[n]=x[n]−x[n−1] emphasizes which region?
A High frequencies
B DC only
C Low frequencies
D Nyquist bin only
Answer: A. High frequencies. This first-difference filter has a zero at DC and attenuates slowly varying components.
Frequency-selective design with more FIR taps can achieve what?
A Higher sampling rate
B Fewer input samples
C Sharper transition
D Zero group delay
Answer: C. Sharper transition. Increasing filter length gives more design freedom and can sharpen the transition region.
After zero insertion during interpolation, which filter removes spectral images?
A High-pass filter
B Low-pass filter
C Notch filter
D All-pass filter
Answer: B. Low-pass filter. Upsampling creates spectral images; an interpolation low-pass filter suppresses them.
As a pole approaches the unit circle from within, what happens to decay?
A It becomes slower
B It becomes faster
C It stops immediately
D It becomes periodic
Answer: A. It becomes slower. A pole nearer the unit circle produces a more slowly decaying natural response.
How does an LTI system form output from its impulse response?
A Correlation with input
B Sampling the input
C Quantizing the output
D Convolution with input
Answer: D. Convolution with input. For an LTI system, output equals the convolution of its input with the impulse response.
Impulse invariance starts from which analog-domain representation?
A Analog frequency bins
B Digital pole table
C Analog impulse response
D Windowed DFT
Answer: C. Analog impulse response. Impulse invariance samples the analog system’s impulse response to construct a digital filter.
Summing the coefficients of a FIR gives its gain at what frequency?
A Nyquist only
B Every frequency
C The pole angle
D DC
Answer: D. DC. At ω=0, all exponential factors equal one, so the FIR response equals the coefficient sum.
Real-coefficient filters with a complex pole also contain what?
A Repeated real pole
B Complex conjugate pole
C Zero at infinity
D Pole at DC
Answer: B. Complex conjugate pole. Real polynomial coefficients require nonreal roots to occur in complex-conjugate pairs.