Signals & Modulation
Follow one 20.0 kbit/s condition-monitoring link from its first time record to a waveform proposal that another engineer can inspect, simulate, and measure.
- Sequence
- 7 modules
- Practice
- 7 decision labs
- Estimated effort
- 9–11 hours
- Recurring case
- 20.0 kbit/s · 2.450 GHz
Choose a waveform by evidence, not by label.
The path builds one versioned waveform decision record. Every new representation must state its convention, units, observation, and engineering purpose before it earns a place in the design argument.
Engineers and serious learners who already own the RF Fundamentals path outcomes.
Frequency, phase, RMS power, dB chains, impedance, and thermal-noise density.
- Move deliberately among time, frequency, I/Q, sample, symbol, eye, constellation, CCDF, and error-vector views.
- Turn an information-rate and channel constraint into a convention-complete waveform proposal.
- Predict first-order spectral and waveform consequences before running a calculation.
- Name the assumptions, reference plane, normalization, and measurement method behind each result.
Seven modules. One reviewable waveform proposal.
Module availability is reviewed independently. An available module opens that lesson; it is not a claim that the complete path or capstone is released. Planned modules remain visible as the dependency map until their own implementation review, without links to placeholder lesson pages.
- 01
Seeing Signals in Time & Frequency
Predict spectral structure, separate a waveform from its finite record, and choose a bandwidth definition that fits the decision.
Open module10 sections
- One signal, three incompatible bandwidth claims
- Classify signal and observation
- Complex exponentials
- Fourier series for repetition
- Fourier transform for an isolated waveform
- Transform properties
- Finite records and windows
- Spectrum and PSD normalization
- Bandwidth as a measurement
- Waveform decision record v1
- 02
Why Modulation Exists
Connect information, antennas, sharing, propagation, and hardware constraints to the need for passband waveforms.
Open module10 sections
- The impossible direct-to-antenna proposal
- Baseband information and DC boundaries
- Frequency translation preserves the recoverable envelope
- Carrier frequency is a system choice
- Sharing spectrum and separating users
- Carrier degrees of freedom
- What a modulation family spends
- Frequency and phase knowledge have a price
- Separate carrier and mapping decisions
- Waveform decision record v2
- 03
I/Q & the Complex Envelope
Use I and Q as an unambiguous coordinate system linking baseband calculations to a real RF waveform.
Open module10 sections
- The sideband that moved to the wrong side
- Why a real RF signal has redundant spectral halves
- I and Q are orthogonal coordinates
- Reconstruct RF under one explicit sign convention
- Upconversion and spectral translation
- Downconversion, filtering, and scaling
- Magnitude, phase, and instantaneous frequency
- Spectral inversion and metadata failures
- I/Q imbalance, DC offset, and LO leakage
- Validate the I/Q contract
- 04
Sampling & Digital Representation
Choose real or complex sample plans and expose the analog assumptions hidden behind a digital record.
Open module10 sections
- A clean tone at the wrong frequency
- Sampling creates replicas
- Nyquist is about occupied support
- Real versus complex sampling
- Bandpass sampling and alias zones
- The anti-alias filter boundary
- Quantization, clipping, and dBFS
- Quantization error is not always white
- Clock error versus jitter
- Waveform decision record v4
- 05
Digital Symbols & Constellations
Move from bits to symbols, mappings, normalized constellations, and defensible SNR and Eb/N0 bookkeeping.
Open module10 sections
- More bits did not create free range
- Bits, symbols, labels, and rates
- Common constellation families
- Normalize before comparing
- Noise clouds and decisions
- Gray labels and bit consequences
- Energy and SNR bookkeeping
- Analytical reference versus simulation
- Structured impairments are not AWGN
- Waveform decision record v5
- 06
Pulse Shaping, ISI & Decisions
Control occupied spectrum and decision quality with pulse shape, roll-off, timing, and matched filtering.
Open module10 sections
- Rectangular symbols fail the spectrum decision
- From a symbol sequence to a waveform
- Rectangular pulse and sinc cost
- Zero ISI applies at sample instants
- Raised-cosine roll-off
- Split the response with RRC filters
- Finite span, delay, and transients
- The eye folds decision history
- Timing, channel ISI, and noise
- Waveform decision record v6
- 07
Modulation Quality & Waveform Tradeoffs
Use EVM, error vectors, CCDF, and impairment signatures to compare waveform choices without hiding conditions.
Open module10 sections
- One EVM, two failures
- Define EVM and reference processing
- EVM summary and conditional views
- Noise and interference signatures
- Frequency, phase, I/Q, and DC signatures
- Compression and regrowth
- Timing and ISI fingerprints
- PAPR and CCDF population
- Counterfactual diagnosis
- Final waveform decision record
Optional explorationExplore the waveform decision arc
See how the seven modules build one waveform argument in dependency order.
Explore the waveform decision arc
See how the seven modules build one waveform argument in dependency order.
Build the waveform argument in dependency order.
Each module adds one auditable decision. Later views depend on earlier conventions, so the path never treats an attractive plot as a substitute for a defined model.
- 01RepresentSignal class, observation, spectrum, bandwidth
- 02TranslateWhy a passband waveform is needed
- 03CoordinateI/Q convention and RF mapping
- 04SampleDigital record and analog boundary
- 05MapBits, symbols, and decision regions
- 06ShapePulse, roll-off, timing, and ISI
- 07VerifyEVM, peaks, impairments, and tradeoffs
Optional explorationCheck the prerequisites
Use six ungraded questions to identify any RF Fundamentals concepts worth revisiting.
Check the prerequisites
Use six ungraded questions to identify any RF Fundamentals concepts worth revisiting.
Check the foundation before adding Fourier tools.
Answer from memory, then reveal each model answer. Four or fewer solid answers suggests a targeted review of RF Fundamentals; it does not block entry.
01Convert 2.45 GHz to period and free-space wavelength.
About 408 ps and 122.4 mm.
02Distinguish peak, RMS, and average power for a sinusoid.
For a zero-offset sine, Vrms = Vpk/√2; average power additionally requires the load and reference plane.
03Combine +12 dB gain, −3 dB loss, and +8 dB gain.
+17 dB net gain.
04Interpret 90° of phase at one frequency.
It is one quarter of that frequency's period of delay, with sign depending on the stated convention.
05State what −174 dBm/Hz assumes.
The approximate available thermal-noise density of a matched source near 290 K.
06Distinguish mismatch from attenuation.
Mismatch redistributes incident power between accepted and reflected waves; attenuation dissipates or otherwise removes forward power along a path.
Optional explorationTry the path capstone
Use the path to prepare a waveform decision record and a review-ready handoff.
Try the path capstone
Use the path to prepare a waveform decision record and a review-ready handoff.
Defend a waveform decision record.
Starting from a 20.0 kbit/s information stream and an illustrative 2.450 GHz carrier, propose a waveform while making every plane, scale, normalization, and open question visible.
90 minutes · evidence portfolio · review-ready handoff01Information source
Document the 20.0 kbit/s source, framing assumptions, and latency constraints before choosing a modulation name.
02Waveform proposal
Specify the mapping, symbol rate, pulse shape, roll-off, I/Q convention, sample plan, and reference planes.
03Evidence
Provide checked time, spectrum, constellation, eye, CCDF, and error-vector views with units and normalization.
04Handoff
Separate what the waveform study establishes from open hardware, propagation, measurement, technology, and compliance questions.