E8 Signals and Emissions

A. Fourier analysis

Fourier analysis breaks any repeating waveform into a sum of sine waves at the fundamental frequency and its harmonics. For an ideal square wave it shows the fundamental plus only the odd harmonics (3rd, 5th, 7th and so on), each with an amplitude of 1/n of the fundamental.

• B. Vector analysis works with quantities that have both magnitude and direction; it does not decompose a waveform into harmonics.
• C. Numerical analysis is the general study of approximate computation methods, not the specific technique for finding a waveform's harmonic content.
• D. Differential analysis is not the name of a technique for breaking a waveform into its sine-wave components; that is Fourier analysis.

A. Successive approximation

A successive-approximation converter finds the digital value one bit at a time, starting with the most significant bit: an internal digital-to-analog converter produces a trial voltage, a comparator checks it against the input, and each bit is kept or cleared. It is a common type of analog-to-digital converter.

• B. Harmonic regeneration is not a method of converting an analog voltage to a digital number.
• C. Level shifting moves a signal's DC level (for example between logic families); it does not digitize the signal.
• D. Phase reversal inverts a signal; it does not convert an analog value into a digital code.

B. Amplitude at different times

A time-domain description shows how a signal's amplitude changes over time, as an oscilloscope displays it. A frequency-domain description, as on a spectrum analyzer, shows amplitude versus frequency instead.

• A. Power at intervals of phase is not a time-domain description; the time domain plots amplitude against time.
• C. Frequency at different times describes a time-frequency display such as a waterfall, not a time-domain signal.
• D. A string of discrete impulses describes a sampled or pulse signal, not the general meaning of the time domain, which is amplitude at different times.

B. A small amount of noise added to the input signal to reduce quantization noise

Dither is a small amount of noise deliberately added to an analog-to-digital converter's input. It randomizes the quantization error so it no longer correlates with the signal, reducing the distortion and spurious products that quantization would otherwise create, especially for low-level signals.

• A. A converter that cannot settle on a value has a fault condition; dither is noise added on purpose.
• C. Irregular quantization step size is a nonlinearity error of the converter, not dither.
• D. Decimation reduces the sample rate by keeping every Nth sample after filtering; it does not skip samples at random, and it is not dither.

D. RMS is measured for both sinusoidal and non-sinusoidal signals

An average-responding meter is calibrated to read correctly only for pure sine waves. A true-RMS meter calculates the actual root-mean-square value, so it reads correctly for non-sinusoidal waveforms such as square waves, pulses and distorted signals as well as sine waves.

• A. An inverse Fourier transform converts a spectrum back into a time waveform; it has nothing to do with true-RMS voltage measurement.
• B. A true-RMS meter reports the RMS value of the waveform; it does not calculate a separate noise factor.
• C. A phasor needs both magnitude and phase, and an RMS reading gives only magnitude, so it cannot be converted directly into phasor form.

A. 2.5 to 1

Speech has occasional peaks with lower-level sounds and pauses between them, so the average power of an unprocessed SSB voice signal is well below its peak envelope power. The typical PEP-to-average ratio is about 2.5 to 1; speech processing raises the average and lowers this ratio.

• B. 25 to 1 is ten times the typical ratio for unprocessed SSB speech.
• C. A 1 to 1 ratio describes a constant-amplitude signal, such as FM or a steady carrier, not SSB voice.
• D. 13 to 1 is far higher than the typical ratio of about 2.5 to 1 for unprocessed SSB speech.

B. Speech characteristics

An SSB signal's envelope follows the voice, so the ratio of peak to average power comes from the characteristics of speech itself: its peaks, pauses and the way energy is spread over syllables. Different voices and speaking styles give different ratios.

• A. The modulating frequency affects where the sideband energy falls, not the ratio of peak to average power.
• C. Carrier suppression removes the carrier, but the remaining envelope still follows speech, which sets the ratio.
• D. Amplifier gain scales peak and average power by the same factor, so it does not change their ratio.

C. Very high speed allows digitizing high frequencies

A flash (direct) converter compares the input with every quantization level at once using a bank of comparators, so it produces a result in a single step. That very high speed allows it to sample at rates high enough to digitize RF signals directly, which a software defined radio needs.

• A. Flash converters need a comparator for every level, so they tend to draw relatively high power; low power consumption is not their advantage.
• B. Out-of-sequence coding is not a reason for using flash converters; their advantage is conversion speed.
• D. Only the high-speed statement is correct, so not all the choices are correct.

D. 256

Each added bit doubles the number of levels a converter can represent, so an N-bit converter encodes 2^N levels. For 8 bits, 2^8 = 256 levels (codes 0 through 255).

• A. 8 is the number of bits, not the number of levels; 8 bits give 2^8 = 256 combinations.
• B. The number of levels depends only on the converter's resolution; an input amplifier's gain does not change it.
• C. Input amplifier gain changes how large a signal fills the converter's range, not the number of levels it can encode.

C. Remove spurious sampling artifacts from the output signal

A digital-to-analog converter's output steps from value to value at the sample rate, creating images and stair-step artifacts at and around multiples of the sampling frequency. A low-pass reconstruction filter after the converter removes these sampling artifacts and leaves a smooth analog signal.

• A. The filter is at the converter's output, not its input, and it does not increase resolution.
• B. A DAC output filter works on the analog output; it does not remove codes from the digital input.
• D. Only removing sampling artifacts is correct, so not all the choices are correct.

A. Total harmonic distortion

An ideal converter reproduces a sine-wave input with no added harmonics, so the total harmonic distortion of the digitized signal is one measure of converter quality. Related specifications include signal-to-noise ratio and spurious-free dynamic range.

• B. Peak envelope power describes a transmitter's output, not the quality of an analog-to-digital converter.
• C. Reciprocal mixing is a receiver problem caused by local oscillator phase noise, not a converter quality measure.
• D. Power factor is the ratio of real power to apparent power in an AC circuit, not a converter specification.

A. The ratio of frequency deviation to modulating signal frequency

The modulation index of an FM signal is the frequency deviation divided by the modulating (audio) frequency. For example, 3 kHz of deviation with a 1 kHz tone gives a modulation index of 3; the index changes as the modulating frequency changes.

• B. The ratio has frequency deviation on top and modulating frequency on the bottom; modulating amplitude over deviation is not the modulation index.
• C. Modulation index does not involve the transmitted bandwidth; it is deviation divided by modulating frequency.
• D. Bandwidth divided by modulating frequency is not the modulation index; the index uses the frequency deviation.

D. It does not depend on the RF carrier frequency

In phase modulation the modulation index is the peak phase deviation in radians, which is set by the amplitude of the modulating signal. The carrier frequency does not enter into it, so the index is the same whatever the RF carrier frequency.

• A. The index does not rise with carrier frequency; it depends on the modulating signal, not the carrier.
• B. The index does not fall with carrier frequency; the carrier frequency does not affect it.
• C. There is no square-root relationship; the modulation index is independent of the carrier frequency.

A. 3

Modulation index = frequency deviation / modulating frequency = 3000 Hz / 1000 Hz = 3. The deviation used is the amount on one side of the carrier, not the total swing.

• B. 0.3 misplaces the decimal point; 3000 Hz divided by 1000 Hz is 3.
• C. 6 results from using the total swing of 6000 Hz instead of the 3000 Hz deviation on one side of the carrier.
• D. 0.6 is a decimal-point error on the total swing; the correct ratio is 3000 / 1000 = 3.

B. 3

Modulation index = frequency deviation / modulating frequency = 6 kHz / 2 kHz = 3. Use the 6 kHz deviation on one side of the carrier, not the 12 kHz total swing.

• A. 0.3 misplaces the decimal point; 6 kHz divided by 2 kHz is 3.
• C. 0.6 does not follow from 6 kHz / 2 kHz, which is 3.
• D. 6 results from using the 12 kHz total swing instead of the 6 kHz deviation on one side of the carrier.

D. 1.67

Deviation ratio = maximum frequency deviation / highest modulating frequency = 5 kHz / 3 kHz = 1.67. Unlike modulation index, it uses the worst-case values for the system, so it is a single number for a given FM system.

• A. 6 does not follow from the ratio of 5 kHz to 3 kHz.
• B. 0.167 misplaces the decimal point; 5 / 3 is 1.67.
• C. 0.6 is the ratio upside down (3 / 5); deviation goes on top.

A. 2.14

Deviation ratio = maximum frequency deviation / highest modulating frequency = 7.5 kHz / 3.5 kHz = 2.14.

• B. 0.214 misplaces the decimal point; 7.5 / 3.5 is 2.14.
• C. 0.47 is the ratio upside down (3.5 / 7.5 = 0.47); deviation goes on top.
• D. 47 does not follow from 7.5 / 3.5; it misreads the inverted ratio of 0.47.

A. Digital modes

OFDM sends data on many closely spaced subcarriers at once, each carrying a slower data stream. Amateurs use it for digital modes, for example the Wi-Fi-based equipment used in amateur mesh networks and some HF data modes.

• B. OFDM is not tied to extremely low-power operation; it is a modulation method for carrying data.
• C. EME (moonbounce) is a propagation path, not something OFDM is specifically used for; weak-signal EME usually uses narrow modes.
• D. OFDM is a data emission and is used on amateur bands where data emissions are authorized.

D. A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference

OFDM divides the data among many subcarriers whose frequencies are spaced so they are mathematically orthogonal and do not interfere with one another. Because each subcarrier carries a slow symbol rate, the long symbols resist intersymbol interference caused by multipath.

• A. OFDM is a digital modulation using orthogonal subcarriers, not a frequency modulation technique using non-harmonically related frequencies.
• B. OFDM is commonly generated with fast Fourier transforms, but it is not a bandwidth compression technique.
• C. OFDM is usually used for wider, higher-speed data; narrow, slow modes are things like PSK31 or FT8.

B. The ratio of the maximum carrier frequency deviation to the highest audio modulating frequency

Deviation ratio is the maximum carrier frequency deviation divided by the highest audio modulating frequency the system allows. For example, 5 kHz deviation with a 3 kHz maximum audio frequency gives a deviation ratio of 1.67.

• A. The carrier center frequency plays no part in deviation ratio.
• C. Deviation ratio does not involve the carrier center frequency; it compares deviation with the highest audio frequency.
• D. Deviation ratio uses the maximum deviation, not the average audio frequency.

B. Dividing the transmitted signal into separate frequency bands that each carry a different data stream

Frequency division multiplexing divides the available spectrum into separate frequency bands (subchannels), each carrying its own information stream at the same time. OFDM is a closely spaced form of it.

• A. Jumping from frequency to frequency at a set rate describes frequency hopping, not FDM.
• C. Dividing a signal into packets describes packet transmission, not frequency division.
• D. Combining streams in a digital combiner and using pulse position modulation does not describe dividing a signal into frequency bands.

B. Two or more signals are arranged to share discrete time slots of a data transmission

In time division multiplexing, two or more signals take turns using the same channel, each in its own repeating time slot. DMR, for example, carries two voice paths on one channel by alternating time slots.

• A. Assigning data streams to separate sub-carriers is frequency division multiplexing, not time division.
• C. TDM does not transmit the time of transmission as a sub-carrier; it gives each signal its own time slot.
• D. Quadrature modulation sends two signals at the same time on carriers 90 degrees apart; it does not divide time into slots.

B. Transmission of data by modulating the amplitude of two carriers of the same frequency but 90 degrees out of phase

QAM transmits data by amplitude modulating two carriers of the same frequency that are 90 degrees apart (in quadrature). Each combination of the two amplitudes is a symbol, so QAM carries several bits per symbol.

• A. QAM is a modulation method, not a data compression technique.
• C. Shifting the phase of the carrier and audio components to produce SSB describes the phasing method of SSB generation, not QAM.
• D. QAM is not an analog video technique using phase modulation and compression; it modulates the amplitudes of two quadrature carriers.

C. The rate at which the waveform changes to convey information

Symbol rate is how many times per second the transmitted waveform changes state (in frequency, phase or amplitude) to convey information. It is measured in baud; each symbol can carry one or more bits.

• A. The number of control characters in a packet is a property of the protocol, not the symbol rate.
• B. How fast forward error correction can make corrections is not the symbol rate.
• D. Characters per second describes throughput of text, not how often the waveform changes state.

A. To minimize bandwidth

If the phase of a PSK signal jumps while the RF voltage is large, the abrupt change produces wide sidebands. Making the change as the RF signal passes through zero avoids that sudden step and keeps the occupied bandwidth to a minimum.

• B. Timing the phase change does not make the modulator simpler; it is done to reduce bandwidth.
• C. Changing phase at the zero crossing has no effect on carrier suppression.
• D. Only minimizing bandwidth is correct, so not all the choices are correct.

C. Use of sinusoidal data pulses

PSK31 shapes its data pulses with a smooth sinusoidal (cosine) envelope, so the amplitude falls gradually to zero at each phase reversal and rises again. Without abrupt changes in amplitude, the signal stays only a few tens of hertz wide.

• A. Zero-sum character encoding is not the technique PSK31 uses to limit bandwidth.
• B. Reed-Solomon is an error-correction code; PSK31 limits bandwidth by pulse shaping, not by its character code.
• D. Pulses with straight-line ramps have sharper corners than sinusoidal pulses, which spreads energy into wider sidebands.

C. 52 Hz

The FCC necessary-bandwidth formula for CW (47 CFR 2.202) is Bn = B x K, where B is the keying speed in baud (about 0.8 x WPM) and K = 5 for fading circuits. At 13 WPM, B = 10.4 baud and Bn = 10.4 x 5 = 52 Hz, which is about 4 Hz per word per minute.

• A. 13 Hz equals the speed in WPM, about one quarter of the 52 Hz bandwidth the formula gives.
• B. 26 Hz is half the bandwidth calculated from Bn = B x K (10.4 baud x 5 = 52 Hz).
• D. 104 Hz is twice the bandwidth calculated from Bn = B x K (10.4 baud x 5 = 52 Hz).

B. 50 Hz

FT8 uses 8-tone frequency shift keying with tones spaced 6.25 Hz apart, so the signal occupies about 8 x 6.25 Hz = 50 Hz.

• A. 10 Hz is narrower than FT8's eight tones spaced 6.25 Hz apart (50 Hz in all).
• C. 600 Hz is much wider than an FT8 signal; many FT8 signals fit side by side in a 3 kHz passband.
• D. 2.4 kHz is about the width of an SSB voice channel, not a single FT8 signal.

A. 15.36 kHz

The FCC formula for FSK telegraphy (47 CFR 2.202) is Bn = 2M + 2DK with M = B / 2 and K = 1.2; since the shift equals 2D, this becomes Bn = B + (1.2 x shift), with B the symbol rate in baud. Here Bn = 9600 + (1.2 x 4800 Hz) = 9600 + 5760 = 15,360 Hz, or 15.36 kHz.

• B. 9.6 kHz counts only the 9600-baud symbol rate and leaves out the frequency shift term.
• C. 4.8 kHz is the frequency shift alone and leaves out the symbol rate.
• D. 5.76 kHz is only the shift term (1.2 x 4800 Hz); the 9600-baud symbol rate must be added.

D. If errors are detected, a retransmission is requested

ARQ (automatic repeat request) detects errors with check codes, and when a block arrives with errors the receiving station asks the sender to transmit it again. Forward error correction (FEC), by contrast, sends redundant data so the receiver can correct errors without asking for a repeat.

• A. Codes that correct errors at the receiver without a repeat are forward error correction, not ARQ.
• B. Polynomial codes that provide automatic correction describe forward error correction, not ARQ.
• C. ARQ does not substitute redundant data; it requests a retransmission of the damaged block.

D. Gray code

In Gray code, consecutive values differ in only one bit, for example 011 to 010 rather than 011 to 100. This prevents large errors when a value is read during a transition and is used in shaft encoders and in mapping bits to modulation states.

• A. Binary coded decimal encodes each decimal digit in four bits, and several bits can change at once (0111 to 1000 for 7 to 8).
• B. EBCDIC is an 8-bit character code used on IBM computers; consecutive codes can differ in several bits.
• C. Extended ASCII is an 8-bit character set; consecutive codes can differ in several bits.

C. Using a more efficient digital code

A more efficient digital code carries more information in the same bandwidth, for example by sending fewer bits for common characters (as PSK31's Varicode does) or by carrying more bits per symbol. The data rate rises while the symbol rate and bandwidth stay the same.

• A. It is possible: a more efficient code sends more information through the same bandwidth.
• B. Higher conversion resolution produces more bits to send for each sample; it does not raise the data rate a channel can carry.
• D. Forward error correction adds redundant bits, which lowers the net data rate for a given bandwidth.

A. They are the same

Baud is the unit of symbol rate: one baud is one symbol per second, so the two are the same thing. The bit rate can be higher than the baud when each symbol carries more than one bit.

• B. Baud does not equal twice the symbol rate; baud is the symbol rate.
• C. Baud is not half the symbol rate; it is the unit of symbol rate.
• D. The code used changes the relationship between bit rate and baud, not between baud and symbol rate.

C. Keying speed and shape factor (rise and fall time)

A CW signal's bandwidth depends on how fast it is keyed and on the shape of each element: faster keying and sharper rise and fall times produce wider sidebands. Properly shaped rise and fall times keep the signal narrow and free of key clicks.

• A. IF bandwidth and Q are properties of a receiver's filters, not of the transmitted CW signal.
• B. Modulation index applies to FM and PM, and output power does not set bandwidth.
• D. Only keying speed and shape factor are correct, so not all the choices are correct.

B. The possible phase and amplitude states for each symbol

A constellation diagram plots each possible symbol of a QAM or PSK signal as a point, with distance from the center showing amplitude and angle showing phase. 16-QAM, for example, shows 16 points, one for each 4-bit symbol.

• A. The constellation shows symbol states on one carrier, not how many carriers are present.
• C. Frequency response is shown on a plot of amplitude versus frequency, not on a constellation diagram.
• D. The constellation shows modulation states, not how many bits the protocol uses for error correction.

C. Internet Protocol (IP)

Amateur mesh networks such as AREDN are computer networks built from radio nodes, and each node has an Internet Protocol (IP) address. Data is routed between nodes using these IP addresses.

• A. Email addresses identify mail users, not network nodes.
• B. A trust server is not how mesh nodes are addressed; they use IP addresses.
• D. Talk groups are used to organize voice traffic on digital voice systems such as DMR, not to address mesh network nodes.

C. Discovery and link establishment protocols

Mesh nodes run discovery and link-establishment (routing) protocols that find neighboring nodes, measure link quality, and build routes automatically. The network then reorganizes itself when nodes join, leave or lose a link.

• A. Forward error correction and Viterbi decoding improve data accuracy on a link; they do not form the network.
• B. Store-and-forward digipeating is a packet radio (AX.25) technique, not how mesh nodes discover each other and build routes.
• D. Code plugs are configuration files for radios such as DMR handhelds, not a way for nodes to form a mesh.

A. Signals not using the spread spectrum algorithm are suppressed in the receiver

A spread spectrum receiver uses the same spreading code (pseudorandom sequence) as the transmitter to collapse the wanted signal back to its original bandwidth. Signals that do not use that code are spread out instead, so most of their energy falls outside the recovered signal's bandwidth and is suppressed.

• B. Spread spectrum does not rely on high power; its energy is spread thinly over a wide bandwidth.
• C. The interference resistance comes from despreading in the receiver, not from error correction codes.
• D. Spread spectrum does not depend on the receiver asking the transmitter to change frequency.

B. Direct sequence

Direct sequence spread spectrum shifts the phase of the RF carrier with a high-speed pseudorandom bit stream (the chip sequence). The fast phase changes spread the signal over a bandwidth much wider than the data alone would need.

• A. Frequency hopping changes the carrier frequency in a pseudorandom pattern rather than shifting the phase with a bit stream.
• C. Binary phase-shift keying is a modulation method; by itself it is not the name of a spread spectrum technique.
• D. Phase compandored spread spectrum is not an actual spread spectrum technique.

D. Rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence

In frequency hopping, the transmitter changes its carrier frequency rapidly according to a pseudorandom sequence, and a receiver that knows the sequence hops in step. Interference on one frequency affects only a small part of the transmission.

• A. Changing frequency when the receiver reports interference describes an adaptive system, not pseudorandom frequency hopping.
• B. Clipping a signal to create harmonics is not spread spectrum and does not provide error correction.
• C. Shifting the carrier phase with a fast pseudorandom bit stream is direct sequence spread spectrum.

C. The generation of key clicks

Turning a CW carrier on or off very abruptly creates wide sidebands on either side of the signal. Listeners on nearby frequencies hear these as clicks, called key clicks.

• A. Very fast rise and fall times do not mainly affect copying the signal; they spread energy onto nearby frequencies.
• B. Harmonics are multiples of the carrier frequency created by nonlinear stages; key clicks are sidebands near the carrier.
• D. Keying edges do not mainly affect tuning; their effect is key clicks heard on nearby frequencies.

A. Increase keying waveform rise and fall times

Key clicks come from keying edges that are too sharp, so the usual cure is to lengthen the rise and fall times of the keying waveform (wave shaping, typically a few milliseconds). Smoother edges narrow the sidebands.

• B. A low-pass filter at the output removes harmonics far from the carrier, but key clicks are sidebands close to the carrier.
• C. Shortening rise and fall times makes keying edges sharper and makes key clicks worse.
• D. A high-pass filter at the output would not remove the sidebands next to the carrier that cause key clicks.

D. Some types of errors can be detected

A parity bit is set so that each character has an even (or odd) number of 1 bits. If a single bit is corrupted in transmission, the parity check fails and the error is detected, although parity cannot show which bit changed or catch an even number of bit errors.

• A. Parity adds a bit to each character, which slightly slows transmission rather than speeding it up.
• B. Parity does not change the signal-to-noise ratio; it only allows some errors to be detected.
• C. The parity bit is used for error checking, so it does not enlarge the character set.

D. Excessive transmit audio levels

AFSK sends audio tones into a transmitter's audio input. If the transmit audio level is set too high, the transmitter is driven past its linear range (on SSB, into heavy ALC action), which distorts the signal and spreads it over a wider bandwidth.

• A. Retries are a result of poor copy at the other station, not a cause of overmodulation.
• B. Too much deviation is the symptom of overdriving an FM transmitter; the usual cause is setting the transmit audio level too high.
• C. Bit errors in a modem affect received data; they do not overmodulate the transmitted signal.

D. Intermodulation Distortion (IMD)

Too much audio drive makes the transmitter nonlinear, creating intermodulation products between the tones of the AFSK signal. Intermodulation distortion (IMD), measured in dB relative to the wanted tones, is the parameter used to evaluate this; many PSK programs display it.

• A. Signal-to-noise ratio compares signal with noise at a receiver; it does not measure distortion from overdriving a transmitter.
• B. Baud error rate is not a standard measure of transmitter distortion.
• C. Repeat Request Rate (RRR) is not a standard measure of AFSK distortion.

D. -30 dB

An idling PSK31 signal is a pair of tones, so any distortion shows up as intermodulation products beside them. An IMD reading of -30 dB, meaning the products are 30 dB below the wanted tones, or a more negative value is generally considered acceptable.

• A. +5 dB would mean distortion products stronger than the wanted signal, an extremely distorted signal.
• B. +10 dB would mean distortion products 10 dB stronger than the wanted signal.
• C. +15 dB would mean distortion products far stronger than the wanted signal.

B. Baudot uses 5 data bits per character, ASCII uses 7 or 8; Baudot uses 2 characters as letters/figures shift codes, ASCII has no letters/figures shift code

Baudot (ITA2) uses 5 data bits per character, which gives only 32 combinations, so it uses two shift characters (LTRS and FIGS) to switch between letters and figures. ASCII uses 7 bits (8 in extended forms), enough for every character without shift codes.

• A. Baudot uses 5 data bits, not 4, and it uses two shift characters (letters and figures), not one.
• C. Baudot uses 5 data bits, not 6, and it is Baudot, not ASCII, that uses letters/figures shift codes.
• D. Baudot uses 5 data bits, not 7, and it is Baudot, not ASCII, that uses letters/figures shift codes.

C. It is possible to transmit both uppercase and lowercase text

ASCII uses 7 bits per character (128 combinations), enough to include both uppercase and lowercase letters along with numbers, punctuation and control characters. Five-bit Baudot has room for only one case.

• A. ASCII has no built-in error correction; an optional parity bit can only detect some errors.
• B. ASCII uses 7 or 8 bits per character, more than 5-bit Baudot, not fewer.
• D. Using a shift character to reach numbers and symbols is a feature of Baudot, not ASCII.