Signal Representation in Communication Questions and Answers

Answer: C

Distortionless transmission needs constant gain and a phase shift proportional to frequency, the latter being simply a constant time delay. Constant phase, by contrast, would delay every component by a different time and so distort the waveform badly. An amplitude proportional to frequency is a differentiator. And time invariance alone is not sufficient: a fixed but frequency-selective response distorts every time.

Answer: D

Nonlinearity mixes the inputs, producing sums and differences of their frequencies and of their harmonics; with two tones the third-order products fall close to the originals and cannot be filtered out, which is why third-order intercept point is a headline receiver specification. A linear filter creates no new frequencies whatever its cut-off. Oversampling is benign. Thermal noise is additive and broadband rather than a product of the input tones.

Answer: A

Group delay is the negative slope of the phase response, and it is the delay experienced by the envelope of a narrowband group of components. Phase divided by frequency is the phase delay, which applies to a single carrier and is a different quantity. The reciprocal of bandwidth is an order-of-magnitude rise time. And a carrier cycle's transit is a propagation matter. A channel with constant group delay across the band is distortionless in phase, which is the practical significance of the definition.

Answer: B

A real cosine has two impulses, one at each of plus and minus the frequency, each of half the amplitude, which is the two-sided representation every modulation calculation uses. A single impulse would describe a complex exponential rather than a real cosine. A continuous band appears only if the tone is observed for a finite time or is not perfectly stable. And harmonics would require a non-sinusoidal periodic waveform such as a square wave.

Answer: C

A symmetric square wave holds only the odd harmonics, with amplitudes falling as one over the harmonic number, which is why its spectrum decays slowly and it demands wide bandwidth. Equal amplitudes at all harmonics would describe an impulse train instead. Even harmonics appear when the waveform loses its half-wave symmetry, for instance when the duty cycle departs from fifty per cent. And a harmonic-free waveform is a pure sinusoid by definition.

Answer: D

An impulse train transforms into another impulse train, spaced by \( 1/T \) in frequency, which is precisely why sampling replicates a signal's spectrum at every multiple of the sampling rate. A single impulse would be a complex exponential. A flat spectrum belongs to a single impulse rather than a train. And odd-only spacing has no basis here; the train is symmetric and every multiple appears with equal weight.

Answer: A

Smoother waveforms have more compact spectra, so the triangular pulse, having no discontinuity in amplitude, decays as the inverse square of frequency where the rectangular pulse decays only as the inverse first power. That is the general rule worth carrying: each additional degree of smoothness in time buys another power of decay in frequency, which is why pulse shaping is used to control the bandwidth of digital transmissions.

Answer: B

A square-law device produces sums and differences, so among the products are

\[ \begin{aligned} f_2 - f_1 &= 200 \ \mathrm{Hz} \\ f_2 + f_1 &= 2200 \ \mathrm{Hz} \end{aligned} \]

along with the second harmonics at 2000 and 2400 Hz. So 200 Hz appears. 1100 Hz is the arithmetic mean of the inputs, which no nonlinearity generates. 2400 Hz does appear as a second harmonic but is not the only new component, so the option as worded is false. 600 Hz corresponds to no combination of the two inputs.

Answer: C

Phase encodes when each component peaks relative to the others, and it is what determines the waveform's shape: two signals with identical amplitude spectra and different phase spectra look completely different in time. Power comes from the amplitude spectrum through Parseval. Bandwidth is the extent of the amplitude spectrum. And signal-to-noise ratio depends on the channel and the receiver rather than on any property of the signal alone.

Answer: D

Cross-correlation slides one signal past the other and reports how alike they are at each relative shift, peaking where they best align. It is the basis of radar ranging, of code acquisition in spread spectrum, and of the matched filter. Power is an autocorrelation quantity at zero lag. Common bandwidth is a spectral overlap rather than a correlation. And phase noise is an oscillator property measured by its own spectrum.