Pulse Modulation Techniques Questions and Answers

Answer: A

The theorem requires at least twice the highest frequency in the signal, and that figure is the Nyquist rate. Sampling at the signal frequency itself loses the waveform entirely. Four times is a practical margin often used but not the theoretical requirement. And the channel's bandwidth is a separate constraint that follows from the pulse rate rather than determining it. Distinguishing a theoretical minimum from the practical rate chosen above it is the first thing to get straight about sampling.

Answer: B

Twice the highest frequency gives 8 kHz, and telephony's familiar 8 kHz sampling rate for a 3.4 kHz channel comes from exactly this calculation with a little margin for the anti-alias filter. 4 kHz is the signal's own limit and would lose everything. 2 kHz is half of it. And 16 kHz is four times, a comfortable practical rate rather than the theoretical minimum. Standard rates in real systems usually sit a little above Nyquist to leave the filter somewhere to roll off.

Answer: C

Aliasing is a component above half the sampling rate reappearing as a lower frequency, indistinguishable from a genuine signal at that frequency, and it is irreversible once it has happened. Amplitude error from the pulse width is the aperture effect. Rounding error is quantisation noise. And channel overlap is crosstalk. Four distinct impairments, and the important property of aliasing is that no processing afterwards can undo it, which is why the filter comes first.

Answer: D

Because aliasing cannot be corrected afterwards, the filter removes anything above half the sampling rate before the sampler can fold it down. Smoothing the recovered waveform is the reconstruction filter's job at the far end. Equalisation and amplitude limiting are separate functions. This is the same principle that governs the receiver's image response: where a stage maps two inputs onto one output, the discrimination has to happen ahead of it.

Answer: A

Under-sampling folds components above half the rate down into the baseband, where they sit on top of the wanted signal. Sample amplitudes are unaffected, and so is the average power. And the reconstruction filter would need to be narrower rather than wider. The damage is done at the moment of sampling, which is why the sampling rate and the anti-alias filter must be settled together as one decision.

Answer: B

In natural sampling the pulse top follows the signal for the duration of the pulse, whereas flat-top sampling holds the value captured at one instant. Flat-top is what a sample-and-hold circuit produces and is far more practical, at the cost of the aperture effect. Spacing is uniform in both. Neither holds the peak. And the rate is a separate choice. The two forms differ in what happens during the pulse, not in when the pulses occur. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: C

The aperture effect is the high-frequency attenuation that flat-top sampling imposes, because a pulse of finite width has a frequency response shaped like a sinc function. It is corrected by an equaliser after the reconstruction filter. Synchronisation loss, sample overlap and rounding error are separate impairments. A finite aperture always costs high frequency response, and the correction is a predictable equalisation rather than a compromise.

Answer: D

A low-pass filter passes the baseband copy and rejects every repeat of the spectrum around the sampling harmonics, which is exactly what the sampling theorem's proof requires. A band-pass filter at the sampling rate would select a repeat rather than the original. A high-pass filter would discard the signal. And a single notch would leave every other repeat in place. Reconstruction is simply selecting one copy from a periodic spectrum, and the copy wanted is the one at baseband.

Answer: A

The height varies with the sample value, which makes the scheme the most direct of the three and also the most vulnerable, since noise adds to amplitude. Duration is the variable in width modulation, and position in position modulation. Pulse count per frame is fixed by the multiplex structure. Which parameter carries the information decides how the scheme behaves in noise, so it is worth naming before anything else about a pulse scheme.

Answer: B

The duration varies while the amplitude stays constant, and that constancy is the source of the scheme's noise immunity: a receiver can clip the pulses to a standard height without losing anything. Height is the amplitude scheme's variable. Frame interval is fixed by the sampling rate. And polarity carries nothing here. Constant amplitude is the property to look for whenever a scheme claims noise immunity.