Signal Processing practice questions

Answer: A) 8 kHz

• ACorrect. Twice the highest frequency.
• BIncorrect. Sample at more than twice.
• CIncorrect. That causes aliasing.
• DIncorrect. That's sufficient but not the minimum.

Answer: B) 10 Hz

• AIncorrect. Divide by N.
• BCorrect. Resolution is \(f_s/N\) = 1,000/100.
• CIncorrect. That's inverted.
• DIncorrect. That's the Nyquist frequency.

Answer: B) Phase only, not its magnitude

• AIncorrect. The magnitude is unchanged.
• BCorrect. A delay multiplies by \(e^{-j\omega t_0}\).
• CIncorrect. Only phase changes.
• DIncorrect. The spectrum's magnitude stays the same.

Answer: A) 20 dB

• ACorrect. \(20\log_{10}(10)\).
• BIncorrect. Voltage ratios use 20 log.
• CIncorrect. That isn't the calculation.
• DIncorrect. That isn't the calculation.

Answer: A) 3 kHz

• ACorrect. \(|f - f_s| = |7 - 10|\) kHz.
• BIncorrect. 7 kHz exceeds the 5-kHz Nyquist limit.
• CIncorrect. Fold back below Nyquist.
• DIncorrect. That's the Nyquist frequency.

Answer: A) \(z^{-1}\)

• ACorrect. The unit delay operator.
• BIncorrect. That's a one-sample advance.
• CIncorrect. That's the Laplace variable.
• DIncorrect. A delay is \(z^{-1}\).

Answer: A) Widens its frequency bandwidth

• ACorrect. Bandwidth is roughly 1/T.
• BIncorrect. Shorter pulses spread in frequency.
• CIncorrect. The spectrum widens.
• DIncorrect. The spectrum widens.

Answer: C) Are always stable and can have exactly linear phase

• AIncorrect. They use past inputs.
• BIncorrect. FIR filters have no feedback poles to destabilize them.
• CCorrect. They usually need more coefficients.
• DIncorrect. They usually need more.

Answer: C) 6

• AIncorrect. It averages three samples.
• BIncorrect. Divide by 3.
• CCorrect. (3 + 6 + 9)/3.
• DIncorrect. It averages three samples.

Answer: A) 12

Linearly convolving sequences of length N and M gives an output of length N + M − 1, which here is 8 + 5 − 1 = 12.

• ACorrect. A linear convolution of lengths N and M has length N + M − 1 = 8 + 5 − 1 = 12. Nonzero outputs run from the first overlap to the last overlap of the two sequences.
• BIncorrect. This adds the two lengths without subtracting 1. The first and last output samples come from a single overlapping sample pair, so the count is N + M − 1.
• CIncorrect. This multiplies the lengths. Convolution slides one sequence past the other, so the output length grows additively, not multiplicatively.
• DIncorrect. This is the length of the longer input only, which is what an 8-point circular convolution would produce. Linear convolution gives a longer output of N + M − 1 samples.