Noise in Analog Systems Questions and Answers

Q: What is the figure of merit for SSB with coherent detection?

SSB also achieves unity, matching DSB-SC, because although it transmits half the sidebands it needs only half the receiver bandwidth, and the two effects cancel exactly. That equality is a satisfying result and often misremembered as SSB being better or worse. Its real advantage over DSB-SC is bandwidth rather than noise. A half or a third would imply a penalty the algebra does not produce.

Q: For wideband FM the figure of merit is proportional to

The standard result is \( \gamma = 3\beta^{2}(\beta+1) \), which for a large index grows as the cube, so a modest increase in deviation buys a large improvement. That is the bandwidth-for-noise trade in algebra. Proportionality to the index alone would understate it badly. The deviation appears through the index rather than on its own. And the message bandwidth enters through the index too. The cube law is why FM broadcasting sounds so much quieter than AM.

Q: For \( \beta = 5 \), the FM figure of merit is about

Substituting into the expression:\[ \gamma = 3 \times 25 \times 6 = 450 \]so about 450, some 26 decibels, against unity for the suppressed-carrier schemes and a third for AM. That single comparison is the whole case for FM broadcasting. 75 uses \( 3\beta^{2} \) without the extra factor. 150 and 25 follow from partial substitutions. The price is a bandwidth of 180 kHz against AM's 10, which is the other half of the trade. Working one numerical case through both schemes side by side fixes the distinction better than any rule of thumb.

Q: Why does envelope-detected AM fall below unity?

The carrier takes at least two thirds of the transmitted power and carries no information, so the output ratio is worse than the channel ratio by that factor. Envelope detection does introduce nonlinearity below threshold, but the factor of three applies well above it. The double bandwidth is shared with DSB-SC, which nevertheless achieves unity. And the quadrature argument describes the detail rather than the dominant cause. Following where the power goes explains the figure of merit directly.

Q: Why does an FM discriminator's output noise rise with frequency?

Frequency is the derivative of phase, so a discriminator differentiates and therefore multiplies the noise spectrum by frequency, giving the triangular output noise that pre-emphasis exists to counter. Integration would produce the opposite slope, which is what a phase detector effectively delivers. The tuned circuits pass the whole baseband. And the limiter acts on amplitude rather than on baseband frequency. One mathematical operation explains the noise shape and hence a whole audio processing convention.

Q: What bounds the FM noise advantage at low signal levels?

Below threshold the output collapses and the improvement vanishes abruptly, so the figure of merit applies only above it. That is why FM coverage boundaries are sharp where AM's fade gradually. Capture concerns two signals rather than one weak one. The pre-emphasis constant shapes the audio. And channel spacing is an allocation. Every gain has a condition attached, and for FM the condition is adequate carrier-to-noise ratio at the detector.

Q: What does the capture effect suppress?

It suppresses the weaker co-channel signal, so the listener hears one programme cleanly rather than two mixed. Baseband noise is dealt with by de-emphasis, amplitude modulation by the limiter, and the image by preselection. Four mechanisms for four different impairments, and attributing an effect to the wrong one is the commonest error in questions on FM noise performance.

Q: A deep-space link has ample spectrum but very little transmitter power. Which scheme suits it?

Wideband FM converts spare bandwidth into output signal-to-noise ratio, which is exactly the trade a power-limited, bandwidth-rich link wants, and its constant envelope allows an efficient saturated amplifier as well. Full-carrier AM wastes power. DSB-SC merely breaks even on noise. And vestigial sideband is chosen for spectral reasons in television. Matching the scheme to which resource is scarce is the whole of modulation selection.

21.

What is the figure of merit for SSB with coherent detection?

A.One half
B.Two
C.One third
D.One

Answer: D

SSB also achieves unity, matching DSB-SC, because although it transmits half the sidebands it needs only half the receiver bandwidth, and the two effects cancel exactly. That equality is a satisfying result and often misremembered as SSB being better or worse. Its real advantage over DSB-SC is bandwidth rather than noise. A half or a third would imply a penalty the algebra does not produce.

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22.

For wideband FM the figure of merit is proportional to

A.The cube of the index
B.The index itself
C.The square of the deviation in hertz
D.The reciprocal of the message bandwidth

Answer: A

The standard result is \( \gamma = 3\beta^{2}(\beta+1) \), which for a large index grows as the cube, so a modest increase in deviation buys a large improvement. That is the bandwidth-for-noise trade in algebra. Proportionality to the index alone would understate it badly. The deviation appears through the index rather than on its own. And the message bandwidth enters through the index too. The cube law is why FM broadcasting sounds so much quieter than AM.

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23.

For \( \beta = 5 \), the FM figure of merit is about

A.25
B.450
C.75
D.150

Answer: B

Substituting into the expression:

\[ \gamma = 3 \times 25 \times 6 = 450 \]

so about 450, some 26 decibels, against unity for the suppressed-carrier schemes and a third for AM. That single comparison is the whole case for FM broadcasting. 75 uses \( 3\beta^{2} \) without the extra factor. 150 and 25 follow from partial substitutions. The price is a bandwidth of 180 kHz against AM's 10, which is the other half of the trade. Working one numerical case through both schemes side by side fixes the distinction better than any rule of thumb.

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24.

Which scheme offers no figure-of-merit improvement over the channel ratio?

A.Phase modulation at large index
B.Narrowband FM at an index of five
C.SSB with coherent detection
D.Wideband FM with pre-emphasis

Answer: C

SSB achieves unity, neither better nor worse than the channel, and DSB-SC matches it. Both angle schemes exceed unity substantially at large index, which is their whole point. And the last option is self-contradictory, since an index of five is wideband rather than narrowband. Recognising that the amplitude family's best case is merely to break even is the clearest way to see why angle modulation displaced it wherever bandwidth allowed. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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25.

Why does envelope-detected AM fall below unity?

A.Envelope detection is inherently nonlinear
B.The receiver bandwidth is twice the message bandwidth
C.Noise adds in quadrature with the sidebands
D.Carrier power contributes nothing to the output

Answer: D

The carrier takes at least two thirds of the transmitted power and carries no information, so the output ratio is worse than the channel ratio by that factor. Envelope detection does introduce nonlinearity below threshold, but the factor of three applies well above it. The double bandwidth is shared with DSB-SC, which nevertheless achieves unity. And the quadrature argument describes the detail rather than the dominant cause. Following where the power goes explains the figure of merit directly.

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26.

Why does an FM discriminator's output noise rise with frequency?

A.It differentiates the phase
B.It integrates the phase
C.Its tuned circuits attenuate low frequencies
D.The limiter removes low-frequency components

Answer: A

Frequency is the derivative of phase, so a discriminator differentiates and therefore multiplies the noise spectrum by frequency, giving the triangular output noise that pre-emphasis exists to counter. Integration would produce the opposite slope, which is what a phase detector effectively delivers. The tuned circuits pass the whole baseband. And the limiter acts on amplitude rather than on baseband frequency. One mathematical operation explains the noise shape and hence a whole audio processing convention.

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27.

What does pre-emphasis and de-emphasis together achieve?

A.Elimination of the capture effect
B.A net improvement in high-frequency signal-to-noise ratio
C.A reduction in the transmitted bandwidth
D.Immunity to the threshold effect

Answer: B

Boosting treble before modulation and cutting it after detection leaves the signal unchanged while attenuating the noise that rose with frequency, a net gain of several decibels at the top of the band. Bandwidth increases slightly rather than reducing, since the boost deepens deviation on bright material. Threshold and capture are unaffected, being properties of the limiter and discriminator. Any matched pre- and post-filter pair works this way when the noise spectrum is not flat.

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28.

What bounds the FM noise advantage at low signal levels?

A.The pre-emphasis time constant
B.The channel spacing in use
C.The threshold effect
D.The capture effect

Answer: C

Below threshold the output collapses and the improvement vanishes abruptly, so the figure of merit applies only above it. That is why FM coverage boundaries are sharp where AM's fade gradually. Capture concerns two signals rather than one weak one. The pre-emphasis constant shapes the audio. And channel spacing is an allocation. Every gain has a condition attached, and for FM the condition is adequate carrier-to-noise ratio at the detector.

Discuss in Forum

29.

What does the capture effect suppress?

A.The noise in the upper part of the baseband
B.Amplitude modulation on the wanted carrier
C.The image frequency ahead of the mixer
D.The weaker of two co-channel signals

Answer: D

It suppresses the weaker co-channel signal, so the listener hears one programme cleanly rather than two mixed. Baseband noise is dealt with by de-emphasis, amplitude modulation by the limiter, and the image by preselection. Four mechanisms for four different impairments, and attributing an effect to the wrong one is the commonest error in questions on FM noise performance.

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30.

A deep-space link has ample spectrum but very little transmitter power. Which scheme suits it?

A.Wideband FM
B.Full-carrier AM
C.DSB-SC
D.Vestigial sideband

Answer: A

Wideband FM converts spare bandwidth into output signal-to-noise ratio, which is exactly the trade a power-limited, bandwidth-rich link wants, and its constant envelope allows an efficient saturated amplifier as well. Full-carrier AM wastes power. DSB-SC merely breaks even on noise. And vestigial sideband is chosen for spectral reasons in television. Matching the scheme to which resource is scarce is the whole of modulation selection.

Discuss in Forum

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