Pulse Modulation Techniques Questions and Answers

Q: What does a reconstruction filter's cut-off frequency have to satisfy?

The filter must pass the whole signal band while rejecting the first spectral repeat, so its cut-off sits between the signal's top frequency and half the sampling rate. That window is exactly what oversampling widens, which is why a higher rate makes the filter cheaper. Cutting off above half the rate would admit the repeat, and cutting below the signal band would discard part of the signal. A requirement bracketed from both sides always has a window whose width is itself a design variable.

Q: Why does oversampling simplify the anti-alias filter?

Sampling well above Nyquist moves half the sampling rate far above the signal band, so the filter has a wide transition region and need not be steep. Word length is a separate matter, quantisation noise per unit bandwidth is unchanged by the rate alone, and the signal's bandwidth is a property of the signal. Buying an easier filter with a faster clock is a trade that became attractive as digital circuitry got cheap and precision analogue filters did not.

Q: The same link develops sharp clicks that grow more frequent as the path degrades. What does this indicate?

Clicks that track path quality are bit errors: a corrupted bit changes a sample's value abruptly and the decoder reproduces that jump faithfully. Quantisation noise is a steady hiss unaffected by the path. Slope overload distorts loud, fast passages rather than producing isolated clicks. And aliasing produces spurious tones. Whether a symptom follows the path or follows the signal is the single most informative observation about a digital link. The parameter that varies and the parameter that does not are worth naming before any substitution is attempted.

Q: A telemetry receiver delivers every sensor's reading to the wrong display. Which fault fits?

Everything wrong and nothing missing is the signature of a slot count offset: the receiver is decoding each slot as its neighbour. A failed sensor would corrupt one channel only. Narrow filters would dull every reading without misrouting any. And a word length error would scale the values rather than swap them. A fault that affects every channel equally and in the same way almost always lies in the framing rather than in the channels. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

Q: A delta modulated link reproduces quiet passages cleanly but distorts loud, high-pitched sounds. Which explanation fits?

Loud and high-pitched together means steep, so the input's slope is exceeding the step size times the clock rate. Granular noise is the opposite failure and shows up on quiet or steady passages. Aliasing would produce spurious tones rather than distortion tracking loudness and pitch. And bit errors would not correlate with the signal at all. The two delta modulator defects can be told apart purely by which passages they spoil, which is why the symptom description is enough to name the cure.

Q: Which change would cure that distortion?

A larger step raises the slope the staircase can follow, and a faster clock would do the same; adaptive delta modulation varies the step automatically for exactly this reason. A narrower filter would dull the output without helping the tracking. A longer hold does not enter into it. And a slower clock would make matters worse by reducing the slope limit further. Once a limit is expressed as a product, every factor in it is a candidate remedy, and the cheapest one wins.

Q: What is the trade-off in choosing a delta modulator's step size?

A step too small causes slope overload on fast signals, and a step too large causes granular noise on steady ones, so the parameter has an optimum rather than a direction of improvement. The other pairings are real trades elsewhere in the system but not the one the step size decides. Whenever a parameter is squeezed from both sides, adaptive control of it is the natural next step, and that is exactly how adaptive delta modulation came about. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Q: Which pulse scheme requires the least receiver complexity?

Width modulation needs only a low-pass filter, since its average value is the message - which is why it appears in the simplest control applications. Code modulation needs a decoder and framing, adaptive delta modulation needs a matched adaptive decoder, and position modulation needs slot timing. Ranking schemes by receiver complexity often reverses the ranking by performance, and which ranking matters depends entirely on where the equipment has to sit.

Q: Which scheme would suit a link where the receiving equipment must be extremely simple?

Width modulation is the answer, for the same reason as before: a filter is the whole demodulator. The three alternatives all need decoders, timing recovery or adaptation logic at the far end. Where one end of a link must be cheap and the other may be expensive, the scheme chosen should put the complexity at the expensive end, and this is the clearest example of that principle in the pulse family.

91.

What does a reconstruction filter's cut-off frequency have to satisfy?

A.Above the signal band and below half the sampling rate
B.Above half the sampling rate but below the sampling rate
C.Exactly at the sampling rate used by the transmitter
D.Below the signal band, to remove residual pulse energy

Answer: A

The filter must pass the whole signal band while rejecting the first spectral repeat, so its cut-off sits between the signal's top frequency and half the sampling rate. That window is exactly what oversampling widens, which is why a higher rate makes the filter cheaper. Cutting off above half the rate would admit the repeat, and cutting below the signal band would discard part of the signal. A requirement bracketed from both sides always has a window whose width is itself a design variable.

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92.

Why does oversampling simplify the anti-alias filter?

A.The signal's own bandwidth is reduced by the higher rate
B.The transition band available becomes much wider
C.Fewer bits are then needed to reach the same quality
D.The quantisation noise falls in direct proportion to the rate

Answer: B

Sampling well above Nyquist moves half the sampling rate far above the signal band, so the filter has a wide transition region and need not be steep. Word length is a separate matter, quantisation noise per unit bandwidth is unchanged by the rate alone, and the signal's bandwidth is a property of the signal. Buying an easier filter with a faster clock is a trade that became attractive as digital circuitry got cheap and precision analogue filters did not.

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93.

A pulse code link produces intelligible speech with a persistent background hiss that does not vary with signal level. Which cause fits?

A.Excessive noise on the transmission path between regenerators
B.An anti-alias filter cutting off below the signal's top frequency
C.Too few quantisation levels in the coder
D.Loss of frame synchronisation at the receiving end

Answer: C

A hiss present at all levels and unaffected by them points at quantisation noise, which is generated inside the coder and rides along with the signal. Lost synchronisation would render the speech unintelligible rather than merely hissy. Path noise would be removed by the regenerators unless it were severe enough to cause errors, which sound like clicks. And a low filter cut-off would dull the speech rather than add noise. Asking whether an impairment varies with signal level separates coder faults from channel faults at once.

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94.

The same link develops sharp clicks that grow more frequent as the path degrades. What does this indicate?

A.Quantisation noise from too coarse a coder
B.Slope overload in the coder's tracking loop
C.Aliasing of components above half the sampling rate
D.Bit errors on the transmission path

Answer: D

Clicks that track path quality are bit errors: a corrupted bit changes a sample's value abruptly and the decoder reproduces that jump faithfully. Quantisation noise is a steady hiss unaffected by the path. Slope overload distorts loud, fast passages rather than producing isolated clicks. And aliasing produces spurious tones. Whether a symptom follows the path or follows the signal is the single most informative observation about a digital link. The parameter that varies and the parameter that does not are worth naming before any substitution is attempted.

Discuss in Forum

95.

A telemetry receiver delivers every sensor's reading to the wrong display. Which fault fits?

A.The frame count has slipped by one slot
B.One channel's sensor has failed open circuit
C.The anti-alias filters have been set too narrow
D.The coder's word length has been misconfigured

Answer: A

Everything wrong and nothing missing is the signature of a slot count offset: the receiver is decoding each slot as its neighbour. A failed sensor would corrupt one channel only. Narrow filters would dull every reading without misrouting any. And a word length error would scale the values rather than swap them. A fault that affects every channel equally and in the same way almost always lies in the framing rather than in the channels. Most errors on this topic come from carrying a result across from a neighbouring scheme where it does not hold.

Discuss in Forum

96.

A delta modulated link reproduces quiet passages cleanly but distorts loud, high-pitched sounds. Which explanation fits?

A.Bit errors introduced along the transmission path
B.Slope overload on the steepest waveforms
C.Granular noise from too small a step size
D.Aliasing caused by an inadequate clock rate

Answer: B

Loud and high-pitched together means steep, so the input's slope is exceeding the step size times the clock rate. Granular noise is the opposite failure and shows up on quiet or steady passages. Aliasing would produce spurious tones rather than distortion tracking loudness and pitch. And bit errors would not correlate with the signal at all. The two delta modulator defects can be told apart purely by which passages they spoil, which is why the symptom description is enough to name the cure.

Discuss in Forum

97.

Which change would cure that distortion?

A.A longer holding time in the sampler
B.A slower clock at the coder
C.A larger step size
D.A narrower reconstruction filter

Answer: C

A larger step raises the slope the staircase can follow, and a faster clock would do the same; adaptive delta modulation varies the step automatically for exactly this reason. A narrower filter would dull the output without helping the tracking. A longer hold does not enter into it. And a slower clock would make matters worse by reducing the slope limit further. Once a limit is expressed as a product, every factor in it is a candidate remedy, and the cheapest one wins.

Discuss in Forum

98.

What is the trade-off in choosing a delta modulator's step size?

A.Bit rate against the number of channels carried
B.Aliasing against the reconstruction filter's steepness
C.Bandwidth against the transmitted average power
D.Slope overload against granular noise

Answer: D

A step too small causes slope overload on fast signals, and a step too large causes granular noise on steady ones, so the parameter has an optimum rather than a direction of improvement. The other pairings are real trades elsewhere in the system but not the one the step size decides. Whenever a parameter is squeezed from both sides, adaptive control of it is the natural next step, and that is exactly how adaptive delta modulation came about. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

99.

Which pulse scheme requires the least receiver complexity?

A.Pulse width modulation
B.Pulse code modulation
C.Delta modulation with adaptive stepping
D.Pulse position modulation

Answer: A

Width modulation needs only a low-pass filter, since its average value is the message - which is why it appears in the simplest control applications. Code modulation needs a decoder and framing, adaptive delta modulation needs a matched adaptive decoder, and position modulation needs slot timing. Ranking schemes by receiver complexity often reverses the ranking by performance, and which ranking matters depends entirely on where the equipment has to sit.

Discuss in Forum

100.

Which scheme would suit a link where the receiving equipment must be extremely simple?

A.Pulse position modulation with framing
B.Pulse width modulation
C.Pulse code modulation with companding
D.Adaptive delta modulation with variable stepping

Answer: B

Width modulation is the answer, for the same reason as before: a filter is the whole demodulator. The three alternatives all need decoders, timing recovery or adaptation logic at the far end. Where one end of a link must be cheap and the other may be expensive, the scheme chosen should put the complexity at the expensive end, and this is the clearest example of that principle in the pulse family.

Discuss in Forum

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