Learn/ Extra course/Module 6 of 10
Extra Course, Module 6: Signals in Full
Covers NCVEC 2024-2028 Extra Pool, Subelement E8 (Signals and Emissions). Four questions on your exam come from this material.
Ray keys a dead-plain carrier into the dummy load and puts the spectrum display beside the oscilloscope. "One line on the analyzer, one sine wave on the scope. Same signal, two true descriptions. Everything in this module is learning to move between those two views, because every signal you will ever make or measure lives in both."
6.1Fourier's Great Idea, and the Honest Digitizer
Fourier analysis is the mathematical bridge between Ray's two screens: any repetitive waveform can be expressed as a sum of sine waves, a fundamental plus harmonics in the right amounts and phases. Two canonical decompositions the exam checks:
- A square wave is the fundamental plus its odd harmonics (3rd, 5th, 7th...), which is why Section 5.2's switching amplifiers need harmonic filters and why key clicks splatter: sharp edges are high harmonics.
- A sawtooth wave contains the fundamental plus all harmonics, odd and even.
Change the time-domain shape and you have changed the spectrum, and vice versa; they are one object.
The measurement vocabulary carries forward with its reasons: RMS matters because it states a waveform's equivalent heating power (the General definition, now the answer to "why measure RMS at all"), and PEP-versus-average keeps its General-course arithmetic, with one addition worth knowing for real signals: typical SSB voice runs a PEP-to-average ratio around 2.5 to 1, which is why your wattmeter's average needle sits so far below the peaks.
Digitizing a signal honestly obeys Section 5.6's law: sample at twice the highest frequency or faster. One counterintuitive refinement joins it: dither, a small amount of noise deliberately added before analog-to-digital conversion, which breaks up quantization artifacts and improves the converter's effective linearity. Adding noise to increase fidelity is the kind of trick that separates Extra-class intuition from arithmetic: quantization error is correlated with the signal and sounds like distortion; dither randomizes it into benign hiss.
Knowledge Check 6.1
Tap an answer. In your own words first, then check yourself.
1. What harmonics make up a square wave?
2. Why is RMS the standard AC measurement?
3. Why add dither before analog-to-digital conversion?
E8A the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E8A01 What technique shows that a square wave is made up of a sine wave and its odd harmonics?
Answer Fourier analysis
Tip Fourier analysis breaks any repeating wave into sines, and a square wave turns out to be a fundamental plus its odd harmonics.
E8A02 Which of the following is a type of analog-to-digital conversion?
Answer Successive approximation
Tip Successive approximation is an A-to-D method, guessing each bit high or low like a binary search closing in on the voltage.
E8A03 Which of the following describes a signal in the time domain?
Answer Amplitude at different times
Tip Time domain means you plot amplitude against time, the shape you see on a scope. Frequency domain is the spectrum analyzer view.
E8A04 What is “dither” with respect to analog-to-digital converters?
Answer A small amount of noise added to the input signal to reduce quantization noise
Tip Dither is a tiny bit of noise added before sampling, which smears the steps so quantization noise drops instead of rising.
E8A05 What is the benefit of making voltage measurements with a true-RMS calculating meter?
Answer RMS is measured for both sinusoidal and non-sinusoidal signals
Tip A true-RMS meter gives correct heating-equivalent voltage for any shape, sine or not, where averaging meters only fake it on pure sines.
E8A06 What is the approximate ratio of PEP-to-average power in an unprocessed single-sideband phone signal?
Answer 2.5 to 1
Tip Unprocessed SSB voice peaks run about 2.5 times its average power because speech is spiky, not steady.
E8A07 What determines the PEP-to-average power ratio of an unprocessed single-sideband phone signal?
Answer Speech characteristics
Tip What sets the SSB PEP-to-average ratio is your speech characteristics, since voice peaks and pauses decide how spiky the envelope is.
E8A08 Why are direct or flash conversion analog-to-digital converters used for a software defined radio?
Answer Very high speed allows digitizing high frequencies
Tip Flash converters are blazing fast, and that raw speed lets an SDR digitize high RF frequencies directly.
E8A09 How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?
Answer 256
Tip 8 bits gives 2 to the 8th levels, so 256 distinct steps.
E8A10 What is the purpose of a low-pass filter used at the output of a digital-to-analog converter?
Answer Remove spurious sampling artifacts from the output signal
Tip A low-pass filter after the D-to-A smooths the staircase output, stripping the spurious sampling images above the wanted signal.
E8A11 Which of the following is a measure of the quality of an analog-to-digital converter?
Answer Total harmonic distortion
Tip Total harmonic distortion gauges A-to-D quality, since a clean converter adds little spurious harmonic content.
6.2Modulation by the Numbers, and Sharing the Channel
FM finally gets its quantities:
- Modulation index is the ratio of frequency deviation to the modulating frequency, computed instant by instant: 6 kHz of deviation from a 2 kHz tone is an index of 3. Note what it ignores: modulation index does not depend on the RF carrier frequency, only on deviation and audio.
- Deviation ratio is the design-limit version: maximum deviation divided by maximum modulating frequency. The pool's pair: 5 kHz deviation with 3 kHz maximum audio gives 1.67; 7.5 kHz with 3.5 kHz gives 2.14.
These numbers connect straight back to the General course's E1C modulation-index limit of 1.0 below 29 MHz and to Carson's-rule bandwidth: the index is the dial that trades bandwidth for noise immunity.
Sharing one channel among many signals is multiplexing, in three geometries:
- Frequency-division multiplexing (FDM): two or more information streams ride different frequencies simultaneously.
- Time-division multiplexing (TDM): streams take turns in time slots on one frequency, and you have operated it since the Technician course: DMR's two voices per channel is TDM wearing a callsign.
- Orthogonal frequency-division multiplexing (OFDM): many closely spaced subcarriers, mathematically orthogonal so they interleave without interfering, each carrying a slow piece of a fast data stream. Its superpower is resistance to multipath and intersymbol interference: slow symbols on many carriers survive the smearing that would destroy fast symbols on one. OFDM is inside digital television, mesh networking, and the wideband digital voice modes, and it is the reason those systems shrug at reflections that would wreck an analog picture.
Knowledge Check 6.2
Tap an answer. In your own words first, then check yourself.
1. What is the modulation index of an FM signal with 6 kHz deviation from a 2 kHz tone?
2. What is the deviation ratio of a system with 7.5 kHz maximum deviation and 3.5 kHz maximum audio?
3. Why does OFDM tolerate multipath so well?
E8B the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E8B01 What is the modulation index of an FM signal?
Answer The ratio of frequency deviation to modulating signal frequency
Tip FM modulation index is deviation divided by the modulating frequency, so it is deviation over tone frequency.
E8B02 How does the modulation index of a phase-modulated emission vary with RF carrier frequency?
Answer It does not depend on the RF carrier frequency
Tip Phase modulation index is set by the phase shift and audio rate only, so the RF carrier frequency does not change it.
E8B03 What is the modulation index of an FM phone signal having a maximum frequency deviation of 3000 Hz either side of the carrier frequency if the highest modulating frequency is 1000 Hz?
Answer 3
Tip Index = deviation / modulating frequency. 3000 Hz over 1000 Hz equals 3.
E8B04 What is the modulation index of an FM phone signal having a maximum carrier deviation of plus or minus 6 kHz if the highest modulating frequency is 2 kHz?
Answer 3
Tip Index = deviation / modulating frequency. 6 kHz over 2 kHz equals 3.
E8B05 What is the deviation ratio of an FM phone signal having a maximum frequency swing of plus or minus 5 kHz if the highest modulation frequency is 3 kHz?
Answer 1.67
Tip Deviation ratio = max deviation / highest audio. 5 kHz over 3 kHz is 1.67.
E8B06 What is the deviation ratio of an FM phone signal having a maximum frequency swing of plus or minus 7.5 kHz if the highest modulation frequency is 3.5 kHz?
Answer 2.14
Tip Deviation ratio = max deviation / highest audio. 7.5 kHz over 3.5 kHz is 2.14.
E8B07 Orthogonal frequency-division multiplexing (OFDM) is a technique used for which types of amateur communication?
Answer Digital modes
Tip OFDM is a digital mode, spreading data across many tidy subcarriers rather than a single tone.
E8B08 What describes orthogonal frequency-division multiplexing (OFDM)?
Answer A digital modulation technique using subcarriers at frequencies chosen to avoid intersymbol interference
Tip OFDM stacks subcarriers at spacings chosen so each one sits at the others' nulls, avoiding intersymbol interference.
E8B09 What is deviation ratio?
Answer The ratio of the maximum carrier frequency deviation to the highest audio modulating frequency
Tip Deviation ratio is the maximum carrier deviation over the highest audio modulating frequency, the worst-case version of modulation index.
E8B10 What is frequency division multiplexing (FDM)?
Answer Dividing the transmitted signal into separate frequency bands that each carry a different data stream
Tip FDM slices the signal into separate frequency bands, each band hauling its own data stream at once.
E8B11 What is digital time division multiplexing?
Answer Two or more signals are arranged to share discrete time slots of a data transmission
Tip Time division multiplexing hands several signals their own repeating time slots so they take turns sharing one channel.
6.3Digital Signals and Their Geometry
The digital vocabulary, made precise:
- Symbol rate is the rate at which the transmitted waveform changes state, and Module 6 of the General course already taught its law: higher symbol rates require wider bandwidth. Bits and symbols part company when each state change carries multiple bits, which is the entire trick of dense modern modes.
- The bandwidth arithmetic the pool checks: a 13-WPM CW signal occupies roughly 52.8 Hz (bandwidth scales with keying speed, about 4 Hz per WPM); a 170-Hz-shift, 300-baud ASCII signal needs about 0.5 kHz; a 4800-Hz-shift, 9600-baud FSK signal needs about 15.36 kHz. Different modes, one principle: bandwidth follows shift plus speed.
- Gray code orders binary values so that only one bit changes between successive values. Its payoff in modulation: a symbol mistaken for its nearest neighbor corrupts only one bit, converting the likeliest channel error into the smallest data error.
The geometry: a constellation diagram plots a digitally modulated signal's states as points, with phase as the angle and amplitude as the distance from the origin. QPSK draws four points on a circle (phase only, the four shifts from the General course); QAM populates a grid, encoding in both amplitude and phase at once, buying bits per symbol at the price of noise margin. Read a constellation like a target: tight clusters mean a clean channel, smeared clusters mean noise, rotated clusters mean phase trouble. One diagram, a complete diagnosis.
Error protection completes the picture with the General course's FEC generalized: redundancy spent up front (as in FT8's deep coding) buys decoding below the noise, and the harder the channel, the better that trade gets.
Knowledge Check 6.3
Tap an answer. In your own words first, then check yourself.
1. What does a constellation diagram display?
2. Why is Gray code used in digital modulation?
3. What is symbol rate?
E8C the easy way: all 15 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E8C01 What is Quadrature Amplitude Modulation or QAM?
Answer Transmission of data by modulating the amplitude of two carriers of the same frequency but 90 degrees out of phase
Tip QAM uses two carriers at the same frequency but 90 degrees apart, and modulating both amplitudes packs more data per symbol.
E8C02 What is the definition of symbol rate in a digital transmission?
Answer The rate at which the waveform changes to convey information
Tip Symbol rate is how often the waveform changes state to carry information, counted in changes per second.
E8C03 Why should the phase of a PSK signal be changed at the zero crossing of the RF signal?
Answer To minimize bandwidth
Tip Switching PSK phase at the RF zero crossing avoids abrupt jumps, which keeps the occupied bandwidth narrow.
E8C04 What technique minimizes the bandwidth of a PSK31 signal?
Answer Use of sinusoidal data pulses
Tip PSK31 shapes each data pulse as a sinusoid, so the gentle transitions hold the signal to a tiny bandwidth.
E8C05 What is the approximate bandwidth of a 13-WPM International Morse Code transmission?
Answer 52 Hz
Tip CW bandwidth is roughly keying speed times about 4, so 13 WPM lands near 52 Hz.
E8C06 What is the bandwidth of an FT8 signal?
Answer 50 Hz
Tip FT8 is a narrow 8-tone mode that fits in about 50 Hz.
E8C07 What is the bandwidth of a 4,800-Hz frequency shift, 9,600-baud ASCII FM transmission?
Answer 15.36 kHz
Tip FSK FM BW = (1.2 x shift) + baud. (1.2 x 4800) + 9600 = 5760 + 9600 = 15360 Hz, so 15.36 kHz.
E8C08 How does ARQ accomplish error correction?
Answer If errors are detected, a retransmission is requested
Tip ARQ corrects errors by asking for a resend, so a flagged block gets automatically repeated until it arrives clean.
E8C09 Which digital code allows only one bit to change between sequential code values?
Answer Gray code
Tip Gray code changes just one bit between neighbors, so a single misread slips to an adjacent value instead of a wild one.
E8C10 How can data rate be increased without increasing bandwidth?
Answer Using a more efficient digital code
Tip Pack more into each symbol with a more efficient code and the data rate climbs while the bandwidth stays put.
E8C11 What is the relationship between symbol rate and baud?
Answer They are the same
Tip Symbol rate and baud are just two names for the same thing, symbols per second.
E8C12 What factors affect the bandwidth of a transmitted CW signal?
Answer Keying speed and shape factor (rise and fall time)
Tip CW bandwidth grows with keying speed and sharpens with the shape factor, how fast each dot rises and falls.
E8C13 What is described by the constellation diagram of a QAM or QPSK signal?
Answer The possible phase and amplitude states for each symbol
Tip A QAM or QPSK constellation diagram plots the allowed phase and amplitude states, one dot per possible symbol.
E8C14 What type of addresses do nodes have in a mesh network?
Answer Internet Protocol (IP)
Tip Mesh network nodes carry IP addresses, since the mesh is really a self-organizing TCP/IP network.
E8C15 What technique do individual nodes use to form a mesh network?
Answer Discovery and link establishment protocols
Tip Mesh nodes build the network themselves using discovery and link establishment protocols to find and connect to neighbors.
6.4Clean Keying, Codes, and Spread Spectrum
The transmitter-hygiene section, Fourier's idea enforced:
- Key clicks are caused by excessively fast CW rise and fall times: sharp edges are odd harmonics (Section 6.1), and they land on your neighbors. The cure is shaping the keying envelope to a rise and fall of about 5 milliseconds, slow enough to tame the sidebands, fast enough to keep crisp code.
- Overdriven digital modes commit the same sin the analog way: the General course's waterfall sidebars, now understood as intermodulation products of an overdriven audio chain. Digital cleanliness is Module 5's amplifier linearity plus this module's spectral awareness, in daily practice.
Character codes, compared:
- Baudot remains the 5-bit RTTY code from the General course. ASCII is the 7-bit code, and its advantages are practical: upper and lower case, and an optional parity bit enabling simple error detection. One bit of redundancy catches any single-bit error, the cheapest error detection ever invented, and the conceptual seed of everything FEC.
Spread spectrum closes the signals course, the mode Extra rules finally let you transmit (above 222 MHz, 10 watts, from Module 1):
- Direct-sequence spread spectrum (DSSS) multiplies the data by a fast pseudorandom sequence, smearing a narrow signal across a wide band at low density.
- Frequency-hopping spread spectrum (FHSS) changes the carrier frequency per a pseudorandom sequence shared by both stations.
- The interference resistance of both comes from the same lock-and-key mechanism: the receiver, synchronized to the pseudorandom sequence, despreads the desired signal while signals not synchronized to the sequence are ignored or diluted. To everyone else, your signal is a whisper of noise; to your partner, it assembles perfectly. It is the one legal amateur mode that hides in plain sight, which is precisely why the rules fence its power and frequencies.
Knowledge Check 6.4
Tap an answer. In your own words first, then check yourself.
1. What causes key clicks?
2. What advantage does ASCII hold over Baudot?
3. Why does spread spectrum resist interference?
E8D the easy way: all 11 questions, with the right answer
Every pool question in this group. Read the answer, let the tip make it stick.
E8D01 Why are received spread spectrum signals resistant to interference?
Answer Signals not using the spread spectrum algorithm are suppressed in the receiver
Tip Spread spectrum resists interference because the receiver despreads only signals following its code and buries everything else.
E8D02 What spread spectrum communications technique uses a high-speed binary bit stream to shift the phase of an RF carrier?
Answer Direct sequence
Tip Direct sequence is the spread spectrum method where a fast binary bit stream keeps shifting the carrier's phase.
E8D03 Which describes spread spectrum frequency hopping?
Answer Rapidly varying the frequency of a transmitted signal according to a pseudorandom sequence
Tip Frequency hopping jumps the carrier around rapidly following a pseudorandom sequence the receiver already knows.
E8D04 What is the primary effect of extremely short rise or fall time on a CW signal?
Answer The generation of key clicks
Tip Snapping a CW signal on and off too fast generates key clicks, splatter from the sharp edges.
E8D05 What is the most common method of reducing key clicks?
Answer Increase keying waveform rise and fall times
Tip The usual key-click cure is to slow the keying rise and fall times so the envelope eases on and off.
E8D06 What is the advantage of including parity bits in ASCII characters?
Answer Some types of errors can be detected
Tip A parity bit lets the receiver catch some errors by checking whether the count of ones still matches.
E8D07 What is a common cause of overmodulation of AFSK signals?
Answer Excessive transmit audio levels
Tip AFSK overmodulation usually comes from cranking the transmit audio too hot into the rig.
E8D08 What parameter evaluates distortion of an AFSK signal caused by excessive input audio levels?
Answer Intermodulation Distortion (IMD)
Tip Intermodulation distortion, IMD, is the number that flags an AFSK signal driven too hard by excess audio.
E8D09 What is considered an acceptable maximum IMD level for an idling PSK signal?
Answer -30 dB
Tip A clean idling PSK signal should show IMD around -30 dB or better, meaning further down.
E8D10 What are some of the differences between the Baudot digital code and ASCII?
Answer 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
Tip Baudot uses 5 data bits with letters and figures shift codes, while ASCII uses 7 or 8 bits and needs no shift.
E8D11 What is one advantage of using ASCII code for data communications?
Answer It is possible to transmit both uppercase and lowercase text
Tip ASCII's wide code set lets you send both uppercase and lowercase text, which Baudot cannot.
Review: every Exam Anchor from this module
E8A Fourier: any repetitive waveform is a sum of sine waves. Square wave: fundamental plus odd harmonics. Sawtooth: fundamental plus all harmonics. RMS: the equivalent heating power measure. SSB voice PEP-to-average: roughly 2.5:1. Sampling: at least twice the highest frequency. Dither: small added noise that improves ADC linearity by randomizing quantization error.
E8B Modulation index: deviation divided by modulating frequency (6 kHz over 2 kHz = 3), independent of carrier frequency. Deviation ratio: maximum deviation over maximum modulating frequency (5/3 = 1.67; 7.5/3.5 = 2.14). FDM: streams on different frequencies. TDM: streams in time slots. OFDM: many orthogonal subcarriers; resists multipath and intersymbol interference.
E8C Symbol rate: how fast the waveform changes state. Bandwidths: 13-WPM CW about 52.8 Hz; 170-Hz shift 300-baud ASCII about 0.5 kHz; 4800-Hz shift 9600-baud about 15.36 kHz. Gray code: one bit changes between successive values, minimizing the damage of nearest-neighbor symbol errors. Constellation diagram: phase as angle, amplitude as radius. QAM: amplitude and phase together.
E8D Key clicks: too-fast rise and fall; shape to about 5 ms. Baudot: 5 bits; ASCII: 7 bits, upper and lower case, optional parity bit for error detection. DSSS: data multiplied by a fast pseudorandom sequence. FHSS: carrier hops per a pseudorandom sequence. Spread spectrum interference resistance: unsynchronized signals are ignored by the despreading receiver.
Before you move on
Ray's two screens are now one language: you can decompose any waveform into its sine waves, quantify FM by index and ratio, read a constellation like an instrument, compute a digital signal's bandwidth from its shift and speed, and explain why a properly shaped CW signal is an act of neighborliness. The signal is the spectrum; the spectrum is the signal.
Module 7 is the program's other heavyweight: eight questions of antennas and transmission lines, from radiation resistance through the Smith chart.
© 2026 Anthony Pelfanio, K4DIA. All rights reserved.