Spectrum & Signal Analysis

01 / 10

A disappearing spur can indict the analyzer

You add attenuation and a suspicious spur disappears. Did the node improve, or did the measurement change?

The fictional condition-monitoring node and gateway operate around 2.450 GHz. The previous lab-practice lesson established a protected TX chain and kept damage limits separate from fidelity. Now an engineer sees a small spectral component and calls it a DUT defect. Before accepting that conclusion, change one analyzer setting while holding the node and external path fixed.

Think about itIf internal attenuation increases by 10 dB, should an input-corrected analyzer-created IM3 product stay fixed like a real input tone?

Answer

No. In the local small-signal cubic fixture it falls 20 dB after input correction. The external tones stay at −30 dBm each. This is a discriminating control, provided the signal remains observable and automatic coupling has not changed the experiment.

Use a deliberately separate SYN-SA-TWO-v1 waveform: two continuous equal tones at ±100 kHz, each −30 dBm at M0. It replaces the earlier burst waveform for this experiment. It is not a generic QPSK spectrum, a hardware capture, or a named wireless-standard mode. An expected-filter model predicts an internal product at ±300 kHz; a noise floor or strong-tone skirt can still conceal it.

One controlled attenuation change · synthetic two-tone anchor
Quantity	A = 10 dB	A = 20 dB
Each external tone, corrected to M0	−30 dBm	−30 dBm
Each tone at M1, preamp off	−40 dBm	−50 dBm
Internal IM3 product, corrected to M0	−110 dBm	−130 dBm
Analyzer-added density, referred to M0	−150 dBm/Hz	−140 dBm/Hz

Common misconceptionA disappearing spur proves the analyzer created it.

It supports that hypothesis only under the stated controls. A real weak spur can disappear beneath a rising referred floor. Two coherent products can cancel at one phase. A compressed instrument can change several mechanisms at once. Record what changed, what stayed fixed, and what became unobservable.

Engineering decision → record update

Open M08-03-SPUR-PLAN-A with parent M08-02-TX-PLAN-B. Keep the earlier raw data immutable. Add competing origin hypotheses and make “setup-limited” an eligible outcome before looking at the next trace.

02 / 10

Follow the signal through the instrument

At which stage could this component be created, removed, averaged or missed?

Follow the quantity through the instrument. A swept analyzer tunes an LO and measures the power admitted by a resolution filter. An FFT analyzer acquires a finite time record through its analog front end, then transforms windowed samples. A modern instrument can combine those operations. Their similar displays do not make their acquisition histories interchangeable. [SA-BASICS]

1 · R1-TX → M0External loss and protection. The correction belongs to named physical planes.
2 · M0 → A → preampInput attenuation precedes optional gain; each active input needs headroom.
3 · M1 → mixer / LOFrequency conversion can create products and reciprocal-mixing noise.
4a · IF / RBW → detectorSwept path: RF selectivity, envelope/power statistic, video processing.
4b · Anti-alias → ADC → windowFFT path: sample rate, live record, finite window, complex DFT.
5 · Trace / marker / integralDisplay selection and averaging are estimators; retain the original acquisition settings.

This original path sketch is a functional model, not a schematic of the FPC or another product. The selected real reference is the R&S FPC1000/FPC1500 manual, version 13, firmware 1.90+. Its §15.6.3 distinguishes swept and FFT selection with mode-dependent restrictions; §15.8 describes trace/detector coupling. Always inspect the actual firmware, options and settings. [FPC]

Think about itIf the reference level moves upward, must the input mixer level fall?

Answer

Only if that instrument’s coupling changes attenuation or gain. This simulator explicitly makes reference level a plot-only control. Its physical quantities must remain identical. An actual measurement record must state whether automatic input/IF gain was active.

\begin{aligned}P_{\mathrm{M1}} &= P_{\mathrm{M0}} - A + G \\ P_{\mathrm{R1-TX}} &= P_{\mathrm{M0}} + L_{\mathrm{ext}}\end{aligned}

Matched, real positive 50 Ω RF interfaces only. A and Lext are positive losses; G is the optional preamp gain. M0 is the analyzer connector; M1 is the mixer input.

Common misconceptionR3 is another name for the receiver RF input.

R3 is the receiver’s decision boundary. R1-RX is its component RF input; R2 is the antenna feed and S0 the over-the-air boundary. This conducted analyzer lesson cannot convert a trace directly into link sensitivity or an OTA claim.

Engineering decision → record update

Add the complete chain, estimator order, plane transformations, model/options/firmware, and automatic couplings. Record the actual acquisition type independently of the plot title.

03 / 10

Allocate level and dynamic range at each plane

Which input runs out of linearity first, even though the analyzer’s damage limit is respected?

Dynamic range is bounded by several mechanisms: additive noise below, compression and distortion above, and frequency-dependent skirts or spurs in between. A stronger signal elsewhere in the passband can invalidate a small local reading. Preamp gain may improve an input-referred floor while consuming mixer headroom. [DYNAMIC]

\begin{aligned}P_{\mathrm{IM3,M1}}&=3P_{\mathrm{tone,M1}}-2\mathrm{IIP3}\\P_{\mathrm{IM3,M0}}&=P_{\mathrm{IM3,M1}}+A-G\end{aligned}

Synthetic mixer: input IIP3 = 0 dBm and IP1dB = −10 dBm. Ptone is the level of EACH equal tone at M1. The two-tone mean total is Ptone + 10log10(2); it is not a PEP statement.

At A = 10 dB with the preamp off, each tone reaches M1 at −40 dBm. Their total is −36.989700043360 dBm, leaving 26.989700043360 dB below mixer P1dB. The internal product is −120 dBm at M1, then −110 dBm referred to M0. The two main tones share a source here, but their mean powers add over a supplied 1 ms interval containing integer beat periods.

Guard the intercept model before calculating products
Active-stage reserve below input P1dB	Eligible statement
At least 10 dB at every active stage	Small-signal cubic estimate available; masking remains separate.
0 to less than 10 dB	Intercept estimate unavailable; do not extrapolate the cubic law.
Less than 0 dB	Small-signal model invalid; suppress downstream fidelity, noise and trace predictions.

Think about itDoes switching on 20 dB of preamp gain always improve a weak-spur measurement?

Answer

No. It raises mixer drive by 20 dB. The preamp input also has its own fictional P1dB of −20 dBm and needs the same 10 dB model reserve. Its lower noise cannot rescue a front end that is outside the model’s linear domain.

Go deeperRefer every added noise source to the same plane

With preamp off, the synthetic mixer density is −160 dBm/Hz at its input, hence −160+A at M0. With preamp on, sum the watts per hertz corresponding to preamp density −165+A and mixer density −160+A−20. At A10 that sum is −154.864790778920 dBm/Hz. Add external input noise once. Attenuator thermal noise is deliberately omitted; this is not a noise-figure prediction.

Common misconceptionA small-signal reserve check is a safe-input approval.

The fictional 08.2 limits of +10 dBm PEP damage and +5 dBm PEP fidelity, plus conditional zero DC, remain separate. Its protected TX-BURST-B chain has 24.5 dB nominal loss and worst M0 PEP 3.3 dBm. Replacing the waveform or path requires renewed evidence; the local M0 tone fixture does not inherit physical approval.

Engineering decision → record update

Record M0 mean/peak/DC eligibility separately from M1 total and preamp reserve. Preserve the 08.2 path and its review triggers; use a new configuration for any changed loss or source state.

04 / 10

RBW selects frequency and collects noise

Why does narrower RBW lower a noise trace while preserving an isolated CW peak?

The resolution filter selects a neighborhood around each tuned frequency. A single calibrated tone sees the filter’s peak gain. Broadband noise contributes power throughout its passband and skirts. Therefore the relevant noise width is the area under the normalized power response, not just its full 3 dB width. [1MA201]

Think about itReduce Gaussian RBW from 100 kHz to 10 kHz. What happens to −150 dBm/Hz noise and to a calibrated isolated CW tone?

Answer

Expected integrated noise falls exactly 10 dB. The isolated tone’s corrected peak remains fixed. Its displayed shape narrows, and the local settling proxy rises by a factor of 100.

\begin{aligned}H(\Delta f) &= \exp [-4 \ln (2)(\frac{\Delta f}{B})^{2}] \\ B_{\mathrm{ENBW}} &= \int H(f)d f = B\sqrt{\frac{\pi }{4 \ln 2}} \\ P_{\mathrm{display}}(f) &= \sum P_{\mathrm{tone}}H(f-f_{\mathrm{tone}}) + N_{\mathrm{total}}B_{\mathrm{ENBW}}\end{aligned}

B is the FULL 3 dB bandwidth in hertz. H is a unit-peak POWER response; H(±B/2)=1/2. Integrate over frequency offset in SI hertz.

Original Gaussian response to an isolated 0 dBm CW tone at M0. Blue line: frequency-domain values. No values clipped by the display scale.

Noise-only fixture · no analyzer-added contribution
RBW	True ENBW	Expected integrated noise	Recovered density
100 kHz	106446.70194312262 Hz	−99.728677898395 dBm	−150 dBm/Hz
10 kHz	10644.670194312262 Hz	−109.728677898395 dBm	−150 dBm/Hz

Recover the known average density by subtracting 10log₁₀(ENBW/1 Hz) from the integrated noise level. The correction is 50.271322101605 dB for the 100 kHz filter. A noise-marker algorithm may also need a detector correction; its value depends on the actual estimator. Never apply this bandwidth correction to a discrete tone.

Go deeperResolution depends on more than the RBW number

A strong component’s skirt can cover a much weaker neighbor even when two equal tones would show a dip. Window/filter shape, level ratio, additive noise and phase-noise skirts matter. The plot uses 801 uniform samples plus exact tone/product centers and ±RBW/2 points. When that base grid is coarse, the simulator warns you: a marked peak is not proof of resolution.

The original settling proxy is 2 × span/RBW² seconds, with an arbitrary teaching factor of 2. A 1 MHz span gives 0.2 ms at 100 kHz RBW and 20 ms at 10 kHz. It is not an FPC timing specification and is not used for zero span or FFT records.

Common misconceptionSumming all these overlapping RBW readings gives total channel power.

Adjacent filter positions repeatedly include the same input power. A raw sum double-counts it. Use a characterized analyzer integration algorithm or properly normalized PSD bins and their frequency widths.

Engineering decision → record update

Attach RBW definition, ENBW, filter shape, frequency grid, actual settling evidence and noise estimator to the record. Keep the intrinsic product power separate from its displayed skirt-plus-noise reading.

05 / 10

Detection and averaging change the estimator

Two engineers select “average” and obtain different powers. Which mean did each calculate?

A display bucket can contain many samples. Sample, peak, power-average and log-average choose different statistics. Further video filtering or trace averaging can then change that statistic again. A smoother line is evidence of a smoother estimator, not automatically a more accurate measurand.

Think about itFor the fixed bucket [1, 9] mW, will averaging its dBm values reproduce the average RF power?

Answer

No. The logarithm is nonlinear. The power mean is 5 mW, whereas the mean of 0 and 9.542425094393 dBm is only 4.771212547197 dBm.

Original detector subfixture · no random samples implied
Estimator	Operation	Output
Sample-first	Select 1 mW	0 dBm
Bucket peak	Select 9 mW	9.542425094393 dBm
Power average	(1 + 9)/2 = 5 mW	6.989700043360 dBm
Log average	(0 + 9.542425094393)/2	4.771212547197 dBm
RMS voltage, real 50 Ω	sqrt(50 × .005) = .5 V	V²/R = 5 mW

“Sample” is itself instrument-specific: our bucket selects the first sample; FPC §15.8.2 describes its last-sample detector. Its RMS detector also has stated bandwidth conditions. Record the selected implementation instead of treating the label as a universal algorithm. [FPC]

\begin{aligned}z[n] &= \alpha p[n] + (1-\alpha)z[n-1] \\ \alpha &= 1 - \exp (-2\pi B_{\mathrm{video}}\Delta t)\end{aligned}

Original VIDEO-PWR-v1 fixture: linear-power samples [1,1,9,9,1,1] mW, Δt = 0.1 ms, z[0]=p[0]. RBW is fixed at 1 kHz only as context. This is not a model of every instrument’s video-voltage processing.

Compare VBW 1 kHz (ratio 1) with 100 Hz (ratio .1) in the bench. The narrower filter rises more slowly and suppresses the brief high samples. Its RF resolution filter has not become narrower. Trace averaging across acquisitions is another operation; define whether it averages watts, voltage, logarithms or another estimator.

Common misconceptionPeak detection gives true RF peak-envelope power, and a noise correction is always 2.51 dB.

A bucket maximum depends on the sampling and detector chain; it is neither instantaneous RF voltage nor a universally calibrated PEP measurement. A log-noise correction belongs to a specific distribution and processing order. This finite deterministic bucket needs no generic correction.

Engineering decision → record update

Name the statistic and its domain, bucket rule, video response, trace averaging, count and initialization. Keep noise-density, gated mean, period mean and PEP as distinct measurands.

06 / 10

A record defines what can be observed

What information can a one-millisecond record contain, and what can extra FFT points only interpolate?

SYN-SA-FFT-v1 uses two noiseless complex tones at ±5 kHz, each −40 dBm at M0, with zero initial phases. Samples have root-watt units: |x[n]|² is watts. The RF reference is 2.450 GHz and the complex sample rate is 1.024 MS/s. N = 1024 acquires 1 ms; it does not describe a burst capture probability.

\begin{aligned}X[k] &= \sum w[n]x[n] \exp (-\frac{j 2\pi k n}{N_{\mathrm{FFT}}}) \\ w_{\mathrm{Hann}}[n] &= \frac{1}{2} - \frac{1}{2} \cos (\frac{2\pi n}{N}) \\ \mathrm{CG} &= \frac{\sum w}{N} \qquad B_{\mathrm{ENBW}} = \frac{f_{s}\sum w^{2}}{(\sum w)^{2}}\end{aligned}

Forward DFT exp(−j2πkn/Nfft), consistent with exp(+jωt). There is no factor of two for signed complex frequencies. Periodic Hann uses N in its denominator; the symmetric filter-design window uses N−1.

Think about itPad this record to NFFT = 4096. Do two unresolved components now become four times easier to separate?

Answer

No. The frequency grid is 250 Hz, but the record remains 1 ms. Window shape and record length still determine the response. A denser plot can locate its peak more accurately without narrowing it.

Canonical FFT window anchors · bin-centered isolated tones
Window / padding	Coherent gain	ENBW	Native / displayed spacing	Each tone / integrated pair
Rectangular, ×1	1	1000 Hz	1000 / 1000 Hz	−40 / −36.989700043360 dBm
Periodic Hann, ×1	.5	1500 Hz	1000 / 1000 Hz	−40 / −36.989700043360 dBm
Periodic Hann, ×4	.5	1500 Hz	1000 / 250 Hz	−40 / −36.989700043360 dBm

\begin{aligned}A_{\mathrm{tone}}[k] &= \frac{|X[k]|}{\sum w } \\ \mathrm{PSD}[k] &= \frac{|X[k]|^{2}}{f_{s}\sum w^{2}} \\ \frac{\sum \mathrm{PSD}[k] f_{s}}{N_{\mathrm{FFT}}} &= \frac{\sum |w[n]x[n]|^{2}}{\sum w^{2}}\end{aligned}

Tone amplitude applies to an isolated bin-centered tone. PSD uses a different window normalization. Integration uses ALL signed complex bins with width fs/NFFT. SciPy documents the same density/spectrum denominator relationship.

The last expression is the window-weighted time-domain power, the correct Parseval partner. It need not equal an arbitrary unweighted short-record mean. A half-bin variant shifts both tones by +f_s/(2N); the record and window determine scalloping and leakage. Increasing acquired N is separate from increasing padding. [PERIODOGRAM] [HANN]

Go deeperWhy a phase readout can be unavailable

At a vanishing complex bin, phase has no meaningful value. Numerical residuals near machine precision must not become a confident phase measurement. The simulator withholds phase below a declared 10⁻²⁴ relative power threshold and shows both complex coefficients and normalized powers at useful key bins.

Common misconceptionFFT RBW is a second independent knob beside record length and window.

In this model its effective noise bandwidth follows f_s, N and the window sums. Swept RBW and VBW controls are disabled. Anti-alias bandwidth, clipping and capture gaps are separate hardware limitations; a mathematically correct DFT cannot reconstruct information never acquired.

Engineering decision → record update

Record sample-rate/reference evidence, acquired N, NFFT, time gate, periodic window, coherent gain, ENBW, sidedness, units, and raw complex samples. Use full precision in calculations and round only displayed values.

07 / 10

Integrate spectral quantities with consistent units

What exactly is being integrated when a marker reports channel power or occupied bandwidth?

A channel is an explicitly bounded frequency interval. Integrate spectral power density in watts per hertz over that interval, then convert watts to dBm. A wideband sensor includes every signal in its passband; a zero-span method must pass the wanted signal with a characterized filter; a spectral method must normalize the filter or PSD correctly. [CHANNEL]

Think about itCan two −40 dBm components be added as −80 dBm?

Answer

No. Each is 10⁻⁷ W. Their sum is 2×10⁻⁷ W, or −36.989700043360 dBm. Similarly, adding a −40 dBm noise contribution to a −40 dBm signal biases the total indication upward by 3.010299956640 dB.

The independent SYN-SA-PSD-v1 fixture is −80 dBm/Hz over [−10,+10] kHz, −110 dBm/Hz over each adjoining 20 kHz band out to ±30 kHz, and exactly zero elsewhere. It has no analyzer floor or modulation standard attached. Partial edges contribute only their overlapped widths.

\begin{aligned}P_{\mathrm{channel}} &= \int _{\mathrm{channel}}S(f)d f \\ F(f_{\mathrm{L}}) &= .005 \qquad F(f_{\mathrm{H}}) = .995 \\ B_{\mathrm{99\%}} &= f_{\mathrm{H}} - f_{\mathrm{L}}\end{aligned}

The percentile definition uses each tail separately: 0.5% below fL and 0.5% above fH. Integrate in linear watts and interpolate within the flat intervals; this is not a shortest-interval search.

Exact PSD integration anchors · offsets from 2.450 GHz
Measurement	Band or definition	Result
Main channel	[−10,+10] kHz; 20 kHz × 10⁻¹¹ W/Hz	−36.989700043360 dBm
Each adjacent channel	[−30,−10] or [+10,+30] kHz	−66.989700043360 dBm
Adjacent/main convention	10log10(Padj/Pmain)	−30 dB
Main/adjacent reciprocal convention	10log10(Pmain/Padj)	+30 dB
Full support	2.004×10⁻⁷ W	−36.981022828048 dBm
Equal-tail endpoints	0.5% / 99.5% cumulative power	−9919.8 / +9919.8 Hz
99% occupied bandwidth	Upper minus lower endpoint	19839.6 Hz

The two small adjacent regions contribute 4×10⁻¹⁰ W. Each tail target is .005×2.004×10⁻⁷ = 1.002×10⁻⁹ W. After the lower adjacent region’s 2×10⁻¹⁰ W, another 8.02×10⁻¹⁰ W lies in 80.2 Hz of the main band. Hence the lower endpoint is −10000+80.2 = −9919.8 Hz.

Recommendation ITU-R SM.328-12 (September 2025) reproduces the equal-tail occupied-bandwidth definition. Its catalogue was checked as in force on 2026-09-09. Necessary bandwidth concerns the information rate and quality needed by an emission; an applicable limit/procedure is a further requirement. This illustrative 99% result establishes neither. [SM328]

Common misconception99% OBW is just the −3 dB width, and a narrow displayed span is enough.

These are different definitions. Truncating any nonzero support makes the full-support OBW unavailable here. Zero total power also leaves percentile bandwidth undefined. ACPR/ACLR names can use reciprocal signs: always write numerator, denominator, channel edges and any applicable standard procedure.

Engineering decision → record update

Store frequency edges, PSD units/normalization, partial-edge rule, full-support status, quantile convention and ratio sign. Preserve the noise contribution and avoid reporting a signal-only power until its separation is justified.

08 / 10

Bursts require time and frequency evidence

Can a longer capture miss every event while a shorter one catches the target?

SYN-SA-EVENTS-v1 is a separately defined timing fixture: three 1 ms events at [5,6), [15,16) and [25,26) ms within a 30 ms observation horizon. It is a known synthetic schedule, not a generated RF spectrogram. A live acquisition can overlap an event fully, partially or not at all.

Think about itPlan A observes [0,4) ms. Plan C runs for 30 ms but is dead during [4,7), [14,17) and [24,27) ms. Which plan proves that no event occurred?

Answer

Neither. Both miss all three known events. C supplies 21 ms live time but its 9 ms of dead time covers every event. Plan B observes [5,9) ms and captures the first full event in only 4 ms live time, with trigger sensitivity supplied as verified fixture metadata.

Illustrative exact schedule, not a spectrogram or acquired trace. Effective live time excludes dead time and is clipped to the analysis gate.

Canonical timing matrix · exact half-open integer-μs intervals
Plan	Elapsed / live / dead	Full / partial / missed	Captured event time
A: free-run [0,4) ms	4 / 4 / 0 ms	0 / 0 / 3	0 ms
B: triggered [5,9) ms	4 / 4 / 0 ms	1 / 0 / 2	1 ms
C: requested [0,30) minus dead	30 / 21 / 9 ms	0 / 0 / 3	0 ms
Any plan, unknown relative phase	Known exposure only	Unknown	Unknown

\begin{aligned}\text{Live} &= (\cup \text{requested windows} \cap \mathrm{gate}) \setminus (\cup \text{dead windows}) \\ \text{Captured duration} &= \operatorname{length}(\text{event} \cap \text{Live})\end{aligned}

Union overlapping windows before subtraction so exposure is counted once. Endpoints are half-open: [0,5) and [5,6) have zero intersection. The custom planner accepts at most 16 live and 16 dead intervals on a 1 μs grid.

Zero span holds frequency fixed and shows a time-domain detector output through a finite RF filter. A gated spectrum chooses a portion of a real record. A spectrogram computes repeated windowed transforms, so its time resolution, frequency resolution, overlap and missing rows need explicit definitions. A smooth colored waterfall cannot certify gap-free hardware acquisition.

Go deeperTrigger sensitivity is evidence, not a checkbox on the DUT

Record trigger source, threshold, slope, delay, pretrigger, holdoff and the path that carries the event. Verify detection with known events at relevant levels and widths. A common frequency reference does not establish timing alignment. If event phase or trigger sensitivity is unknown, this simulator reports unknown outcomes; it cannot infer a probability from a convenient independent-arrival assumption.

Common misconceptionMax hold eventually proves that no rare spur exists.

Max hold retains only maxima from acquired data. Events during dead time, outside the IF passband or below trigger sensitivity remain unseen. A late gate can discard a real ramp before a spectrum is even calculated.

Engineering decision → record update

Add the live/dead interval ledger, trigger verification, time reference, gate, raw pre/post-trigger samples and an independent gateway event log. Keep an absence claim unavailable unless a stated statistical method and acquisition coverage support it.

09 / 10

Separate close-in noise, spurs, and residual floors

Is the close-in skirt the source’s phase noise, a discrete spur, or the analyzer’s residual?

A phase-noise result compares a sideband density at a declared carrier offset with the carrier power. Direct spectrum measurements can include source and analyzer residuals, AM contributions and discrete spurs. Reciprocal mixing converts strong off-channel energy through LO noise into the observed band; reducing RBW alone may not separate those mechanisms.

Think about itA −20 dBm carrier has −100 dBm of sideband noise in a true 1 kHz ENBW at +10 kHz. Is the normalized result −80 dBc/Hz?

Answer

No. −80 dBc is the integrated sideband/carrier ratio in that bandwidth. Dividing by 1000 Hz subtracts another 30 dB, giving −110 dBc/Hz.

\begin{aligned}\mathcal{L}(+10 \mathrm{kHz}) &= -100 - (-20) - 10\log _{10}(1000) \\ &= -\frac{110 \mathrm{dBc}}{\mathrm{Hz}}\end{aligned}

SYN-SA-PN-v1 is an informative arithmetic example at +10 kHz offset, with true 1 kHz ENBW and a correctly characterized average-noise estimator. It is independent of the Gaussian filter’s RBW. No arbitrary 3 dB correction is inserted.

The SSB convention reports one sideband relative to the carrier. Cross-correlation can reduce uncorrelated instrument contributions; shared source or path noise is not removed by assuming two channels are independent. A residual floor can bound what is observable without determining the DUT’s own phase noise. [PHASE]

Evidence required before attributing a close-in feature
Candidate	Discriminating evidence	Unresolved when absent
Discrete spur	Offset/line shape, calibrated tone estimator, controlled source/DUT state	Noise-density normalization is ineligible on the line.
Internal distortion	Valid headroom, attenuation control, known-source comparison	Slope alone does not establish origin.
Phase-noise skirt	Carrier/offset, true ENBW, detector correction, residual source/analyzer characterization	Reported value may be an aggregate or floor-limited.
Coherent product mixture	Relative phase or controlled coherent-path evidence	Cancellation can mimic a clean spectrum.

Common misconceptionSubtract the analyzer’s phase-noise curve in dB to obtain the DUT curve.

Independent power contributions combine linearly, while correlated contributions need a joint model. Near a residual floor, subtraction is poorly conditioned and its uncertainty can dominate. Without the required evidence, preserve a limited result instead of manufacturing a cleaner DUT spectrum.

Engineering decision → record update

Record carrier power, signed offset, SSB convention, true ENBW, estimator correction, spur exclusions, source/analyzer residuals and their correlation assumptions. A conformance limit and its method remain separate.

10 / 10

Defend two different acquisition plans

Can another engineer reproduce your two acquisition plans and understand what each result cannot establish?

Start with the bench’s missed-burst preset. Predict B and C, apply each, then return to the two-tone fixture and save a baseline before changing attenuation. Repeat the baseline exercise for noise RBW, FFT window and zero padding. Use the explicit unknown and compression states to identify where the evidence stops.

Interactive bench · bounded teaching model

Analyzer Settings Simulator

Predict a change, apply it, then compare the evidence. Choose a complete fixture to change models. These are synthetic expectations and exact schedules, not remote instrument readings.

JavaScript is disabled. The canonical plan A result below is complete and readable; simulator controls require JavaScript. All lesson answers and static measurement records use native disclosure elements.

Complete fixture presetDefault missed-burst plan A. Loading a preset replaces every field and result atomically. Baseline is kept for comparison.

Active model: Exact capture timing. RF RBW and FFT settings cannot alter these exact temporal intersections.

Acquisition settings · capture

Capture planDefault A: [0,4) ms. B: [5,9) with supplied verified trigger. C: 30 ms with three dead intervals. Custom edits the interval lists.

Event timing phaseDefault known fixture schedule. Unknown phase makes capture outcomes and probability unknown.

Trigger evidenceFree-running by default. B needs the supplied verified trigger; unknown sensitivity withholds outcome.

Analysis gate start (ms)0–100 ms; step .001; default 0. Half-open gate; start must precede end.

Analysis gate end (ms)0–100 ms; step .001; default 30. Gate clips requested live windows, never creates capture.

Custom live windows (ms)Required for custom; up to 16 start:end pairs separated by commas. Bounds 0–100, step .001 ms. Default 0:4; overlaps count once. Unavailable in the selected model/fixture; this control does not change its result.

Custom dead windows (ms)Enter none or up to 16 start:end pairs; bounds 0–100, step .001 ms. Default none; subtracted from live windows. Unavailable in the selected model/fixture; this control does not change its result.

Why are the other instrument controls unavailable?

Each model represents a different measurement operation. Inactive settings are shown for orientation and cannot silently change another model’s physics.

Center frequency (GHz)0.100–6.000 GHz; step .001; default 2.450. Frequency label, with exp(+jωt). Unavailable in the selected model/fixture; this control does not change its result.

Spectral span (MHz)0–10 MHz; step .001; spectral default 1. Sweep requires >0; FFT ≤1.024. Capture uses zero span. Unavailable in the selected model/fixture; this control does not change its result.

Internal attenuation A (dB)0, 5, 10, 15, 20, 30 or 40 dB; default 10. Before preamp and mixer. Unavailable in the selected model/fixture; this control does not change its result.

PreampDefault off; on adds 20 dB. Preamp input reserve is checked separately. Unavailable in the selected model/fixture; this control does not change its result.

Display reference level (dBm)−100–30 dBm; step 1; default −10. Plot top only; no automatic attenuation. Unavailable in the selected model/fixture; this control does not change its result.

RBW, full 3 dB width (Hz)1–10,000,000 Hz in decades; default 100,000. Video context fixes RBW at 1,000 Hz. Unavailable in the selected model/fixture; this control does not change its result.

External input density (dBm/Hz)−180–−100; step 1; noise default −150, two-tone −180. At M0; no analyzer floor in isolated-noise fixture. Unavailable in the selected model/fixture; this control does not change its result.

Each external tone at M0 (dBm)−100–0; step 1; swept default −30, FFT −40. Two equal tones; no added FFT noise. Unavailable in the selected model/fixture; this control does not change its result.

External loss Lext (dB)0–40 dB; step .1; default 0. A separate M0 → R1-TX correction, applied once. No change at M1. Unavailable in the selected model/fixture; this control does not change its result.

Product origin fixtureDefault internal. External spurs fixed at −110 dBm at ±300 kHz. Mixed adds coherent fields. Unavailable in the selected model/fixture; this control does not change its result.

External/internal relative phase (°)0–360°; step 1; default 180°. Only the mixed product uses this phase. Unavailable in the selected model/fixture; this control does not change its result.

Bucket estimatorDefault power-average; fixed bucket [1, 9] mW. Sample takes first value. Unavailable in the selected model/fixture; this control does not change its result.

VBW / RBW ratio.01–10; step .01; default 1. Fixed 1 kHz RBW context and .1 ms sample interval; linear-power video filter. Unavailable in the selected model/fixture; this control does not change its result.

FFT windowDefault periodic Hann; rectangular also available. All N samples retained. Unavailable in the selected model/fixture; this control does not change its result.

Acquired samples N256, 512, 1024, 2048 or 4096; default 1024. Fixed fs = 1.024 MS/s. Unavailable in the selected model/fixture; this control does not change its result.

FFT zero-padding factor1, 2 or 4; default 1. Nfft ≤16,384; extra samples are zeros, not observations. Unavailable in the selected model/fixture; this control does not change its result.

FFT tone placementDefault nominal ±5 kHz. Half-bin variant shifts both tones by +fs/(2N); zero initial phases. Unavailable in the selected model/fixture; this control does not change its result.

Canonical default: plan A misses all three events.

Missed burst · A

Committed result

4 ms live; 0 full, 0 partial, 3 missed.

Illustrative exact schedule, not a spectrogram or acquired trace. Effective live time excludes dead time and is clipped to the analysis gate.

Capture exposure and event outcomes
Quantity	Committed result
Observation horizon / gate	0–30 ms event schedule / [0, 30) ms
Elapsed acquisition envelope	4 ms
Live / dead exposure	4 / 0 ms
Captured event duration	0 ms
Event 1 · [5, 6) ms	missed; 0 μs
Event 2 · [15, 16) ms	missed; 0 μs
Event 3 · [25, 26) ms	missed; 0 μs
Event probability	Unknown: no stochastic arrival or independence model.
Trigger	Free-running; known phase only in this fixture

The schedule is in integer microseconds. A touching endpoint has zero duration. Custom windows describe a plan applied to this known schedule; they are not real measurement evidence.

Illustrative / Derived · analyzer-settings-simulator/2.0 · p08-m03-analyzer-fixtures-v1. Real, matched 50 Ω RF interfaces; no physical acquisition, calibrated uncertainty or conformance claim.

Complete committed settings and evidence

Committed configuration · units and representation are in the labels
Setting / condition	Committed value
Model / fixture	capture · Missed burst · A
Capture plan	A
Event timing phase	known
Trigger evidence	free
Analysis gate start (ms)	0
Analysis gate end (ms)	30
Custom live windows (ms)	0:4
Custom dead windows (ms)	none
Acquisition evidence	Supplied synthetic fixture only. Physical safety, calibration, trigger and residual evidence are unresolved except where explicitly supplied by the timing fixture.
Validity	Committed; numeric rounding affects display only.

Print preserves this committed result, its settings, stale-state warning and any baseline. The canonical records below remain fixed independently of custom exploration. Session state is temporary; no saved progress, score or certification is created.

Think about itCan you copy the close-in spur settings directly into a rare-ramp investigation?

Answer

A narrow, settled spectrum can resolve a stable weak line while missing the ramp entirely. A short, wideband capture preserves timing but may lack the window resolution and residual floor needed for the close-in line. Each method needs its own acquisition and evidence record.

Method 1 · A close-in weak spur beside a strong carrier

Question and waveform. SYN-SA-CLOSE-v1 is a continuous −20 dBm carrier at M0 with a candidate −100 dBm line at +10 kHz. Resolve and attribute that line; there is no supplied emissions limit.

Plane and safe input. Reverify the inherited 24.5 dB R1-TX → M0 chain for this new state, including peak/DC/transients and each component’s rating. Record both M0 and corrected R1-TX; internal A is a separate correction. Keep the preamp off initially and establish every active-stage linearity reserve.

Acquisition. Start with a 40 kHz span, 100 Hz Gaussian teaching RBW/106.4467 Hz ENBW and a settled linear-power average. The original proxy is 8 s, not an instrument command. Choose actual sweep/detector/VBW from the selected manual and verify settling. Preserve timing and any dead intervals even for the continuous stimulus.

Controls and decision. Collect A10/A20/A10 at fixed external setup, 10 complete acquisitions per state, plus a characterized source/substitution control. Compare intrinsic line power with carrier skirts and additive/residual floors. Quantify loss/mismatch, calibration, repeatability and residual uncertainty using 08.1. A compatible attenuation trend supports an origin hypothesis; masking or coherent mixing leaves attribution inconclusive.

Evidence to retain. Raw traces or I/Q, complete settings/options/firmware, overload/lock status, path and calibration IDs, timestamps, waveform/state, repeat distribution, correction chain and the predeclared decision rule. M08-03-SPUR-PLAN-A below is the full static record.

Method 2 · A rare gateway-correlated ramp or digital spur

Question and waveform. Search for a short component during wake-up in the same fictional node/gateway. SYN-SA-EVENTS-v1 supplies timing only; TX-BURST-B’s generic QPSK burst is a separately identified RF waveform. Characterize the ramp’s bandwidth instead of assuming the stable carrier describes it.

Plane and safe input. Preserve the 08.2 protected path, its worst M0 PEP of 3.3 dBm, conditional zero-DC evidence and separate fictional damage/fidelity thresholds. New ramp peaks or bias transitions require review. Check input, preamp, mixer and ADC overload during the entire event.

Acquisition. Use zero-span envelope timing with a sufficiently wide characterized RF passband, then a separate complex capture for the spectral question. A candidate 1.024 MS/s, N4096 record lasts 4 ms; a periodic Hann supplies a 375 Hz ENBW. Verify that ±512 kHz anti-alias support includes the target. Preserve pretrigger, threshold, slope, delay, holdoff, gate and missing-frame/dead-time indicators; validate trigger sensitivity using a known event.

Controls and decision. Repeat 30 wake-up trials with a synchronized independent event log and baseline/digital-activity state controls. Compare live overlap, full/partial capture and subsequent gated spectra. Include trigger jitter, timing alignment, transient response and unobserved intervals in the uncertainty/limitations. Without an event-arrival model and verified coverage, no missing-event probability or DUT-absence verdict is available.

Evidence to retain. Raw pre/post-trigger envelope or complex samples, unedited event logs, every live/dead interval, gate/window normalization, source state and the same configuration/calibration provenance as method 1. M08-03-BURST-PLAN-A below preserves the complete plan.

Common misconceptionA screenshot and a settings list are a reproducible measurement record.

They omit the competing hypotheses, applicability conditions, raw-data lineage, corrections, uncertainty and rule that turn an indication into an inference. Keep those with the settings, including every unresolved item.

Two complete, immutable method records

These p08-measurement-record-v1 snapshots reuse 08.1’s field contract. They are illustrative planning artifacts, available without JavaScript and independent of custom bench edits. Earlier raw IDs and their contents are preserved.

M08-03-SPUR-PLAN-A · Close-in spur method

p08-measurement-record-v1 · complete M08-03-SPUR-PLAN-A
Record field	Fixed illustrative snapshot
id	M08-03-SPUR-PLAN-A
parentIds	M08-02-TX-PLAN-B · M08-01-RAW-A
owner	Fictional measurement engineer, condition-monitoring node/gateway team
question	Is the close-in low-level component emitted by the node, or created/masked by the analyzer?
hypotheses	H1: external DUT spur. H2: analyzer intermodulation. H3: coherent mixture. H4: carrier skirt or analyzer/source residual floor.
requirement	REQ-SPUR-EVIDENCE-v1: identify the component’s origin and report its plane, offset and estimator; no emissions limit supplied.
decisionRule	Declare attribution only with consistent one-change controls, valid front-end reserve and quantified masking/residual uncertainty. Otherwise setup-limited/inconclusive.
specimen	SYN-NODE-GATEWAY-SA-A, one fictional 2.450 GHz condition-monitoring node and gateway; no real specimen or population inference.
configuration	CFG-SA-SPUR-A; HW-SYN-A1 / FW-SYN-1.0; continuous-carrier diagnostic mode explicitly replaces portfolio generic QPSK. Generic QPSK is not a named standard radio.
state	Synthetic 3.300 V supply, 25 °C stable laboratory, shielded conducted 50 Ω assembly, fixed cable route; startup excluded. Physical evidence is pending.
timestamp	Fixed illustrative planning snapshot 2026-09-09T00:00:00Z; this is not a browser acquisition timestamp.
environment	25 °C assumption; humidity, ambient RF and long-term drift not supplied. No uncertainty value silently assigned to missing evidence.
stimulus	SYN-SA-CLOSE-v1: continuous −20 dBm carrier at M0, candidate −100 dBm discrete spur at +10 kHz. Distinct from SYN-SA-TWO-v1 (−30 dBm equal tones, ±100 kHz) used to test analyzer IM3.
statistic	Discrete tone power at M0 and corrected R1-TX; carrier-relative dBc separately. Linear-power averaging then dBm, not noise-density normalization on a tone.
population	One fixed node state; planned 10 independent complete acquisitions at each attenuation setting, then a return to baseline. No fabricated sample scatter or confidence interval.
acquisition	Expected swept response, 40 kHz span centered 2.450 GHz; 100 Hz Gaussian RBW (ENBW 106.446701943 Hz); teaching settling proxy 8 s. Actual device sweep/settling must be validated independently.
planes	R1-TX component output → explicitly characterized external path → M0 analyzer connector → A → preamp → M1 mixer. Real positive 50 Ω only. R2 is antenna feed, S0 OTA and R3 receiver decision, excluded.
chain	Planning import CFG-TX-B-B has B1 .5 dB + A1 20 dB + C1 1 dB + A2 3 dB =24.5 dB. Reverify it for the new continuous-carrier state. Arithmetic fixtures use Lext=0 at M0; they do not overwrite the inherited path.
instrument	SYN-SA-A / SIM-003 / SIM-FW-1; fictional Gaussian front end, manual attenuation, optional idealized 20 dB preamp. Actual FPC documentation is orientation only, not a matching hardware claim.
settings	A=10 dB then 20 dB; preamp off; manual reference −10 dBm (display-only in model); linear power average; video smoothing disabled for the expected mean. Actual detector/VBW and auto couplings must be recorded from the selected instrument.
calibration	Synthetic input amplitude correction +A−G occurs once, Lext correction separately once. Cable/DC block/pad transfer, mismatch, amplitude linearity, frequency reference and current verification for this new state remain evidence to collect.
rawEvidence	SYN-SA-CLOSE-v1 and SYN-SA-TWO-v1 immutable stimulus definitions; no physical trace files. Retain raw samples/trace, instrument state/options/firmware, calibration IDs, timestamps and overload flags per acquisition. M08-01-RAW-A and SYN-IND-01 unchanged.
processing	analyzer-settings-simulator/2.0; p08-m03-analyzer-fixtures-v1; float64. Unit-peak Gaussian power response and expected linear-power sums; cubic estimates only ≥10 dB below active-stage P1dB. Separate phase-aware sum for coherent mixed products.
uncertainty	Analytic fixture has no stochastic uncertainty estimate. Actual amplitude calibration, external loss/mismatch, repeatability, settling, frequency error, phase-noise skirt and analyzer-added noise require 08.1 propagation, including shared influences. Finite numerical tolerance is not measurement uncertainty.
result	SYN-SA-TWO-v1: A10 → corrected internal product −110 dBm; A20 → −130 dBm, tones stay −30 dBm. Added analyzer density rises −150 to −140 dBm/Hz. These do not establish the close-in DUT spur’s origin.
inference	The controlled attenuation test can support an internal-origin hypothesis within its linearity assumptions. A floor-limited disappearance or coherent cancellation remains inconclusive without additional controls.
unresolved	Real safe-input eligibility, detector/VBW behavior, instrument residuals, repeat distribution, path calibration and DUT spur power are not measured. No standard emissions limit or conformance verdict.
next	Verify peak/DC ratings and protection in the new state; collect A10/A20/A10 traces plus characterized source/substitution controls. Follow 08.4 for vector fixture evidence when available.
review	New waveform, firmware, gain state, cable movement, overload, unlock or loss of temperature stability invalidates the inference and requires review.

M08-03-BURST-PLAN-A · Rare burst / ramp method

p08-measurement-record-v1 · complete M08-03-BURST-PLAN-A
Record field	Fixed illustrative snapshot
id	M08-03-BURST-PLAN-A
parentIds	M08-02-TX-PLAN-B · M08-03-SPUR-PLAN-A
owner	Fictional measurement engineer, condition-monitoring node/gateway team
question	Can the acquisition capture a rare gateway-correlated ramp or short digital spur, and separate its timing from the wanted burst?
hypotheses	H1: a real digital activity spur during wake-up. H2: an event lies in dead time. H3: trigger threshold/bandwidth or a time gate hides it. H4: analyzer overload during the ramp.
requirement	REQ-BURST-EVIDENCE-v1: demonstrate capture coverage and preserve time-aligned evidence for the chosen event; no event-rate, BER or standard limit supplied.
decisionRule	A known full overlap establishes capture only for the supplied deterministic event. Missing events, unknown phase/trigger sensitivity or dead time prevent an absence claim. Partial overlap is reported as partial.
specimen	SYN-NODE-GATEWAY-SA-A, one fictional 2.450 GHz condition-monitoring node and gateway; no real specimen or population inference.
configuration	CFG-SA-BURST-A; same fictional hardware/firmware, explicit wake-up diagnostic state. SYN-SA-EVENTS-v1 is a binary event schedule, not an FFT waveform or a recreated QPSK modulation.
state	Synthetic 3.300 V supply, 25 °C stable laboratory, shielded conducted 50 Ω assembly, fixed cable route; startup excluded. Physical evidence is pending.
timestamp	Fixed illustrative planning snapshot 2026-09-09T00:00:00Z; this is not a browser acquisition timestamp.
environment	25 °C assumption; humidity, ambient RF and long-term drift not supplied. No uncertainty value silently assigned to missing evidence.
stimulus	SYN-SA-EVENTS-v1: [5,6), [15,16), [25,26) ms in [0,30) ms. Method separately carries inherited TX-BURST-B generic QPSK, 1 ms on / 10 ms period, +20 dBm on-time mean, 6 dB PAPR at R1-TX; timing phase explicitly replaced here.
statistic	Event overlap duration in integer microseconds, full/partial/missed status, live/dead exposure. A subsequent gated RF power/PSD estimate needs its own bandwidth and normalization.
population	Three supplied synthetic events. Plan 30 repeated wake-up trials with raw pre/post-trigger captures and independent event timestamps. No independent-arrival model or probability of intercept supplied.
acquisition	First use zero-span envelope timing with sufficient analog bandwidth to pass the ramp; separately acquire complex 1.024 MS/s records, N4096 (4 ms), periodic Hann for spectral views if the target lies within ±512 kHz. This method does not assume every ramp has been characterized by those bandwidths.
planes	R1-TX component output → explicitly characterized external path → M0 analyzer connector → A → preamp → M1 mixer. Real positive 50 Ω only. R2 is antenna feed, S0 OTA and R3 receiver decision, excluded.
chain	Inherited CFG-TX-B-B 24.5 dB nominal path; worst supplied TX PEP at M0 3.3 dBm, +10 dBm damage and +5 dBm fidelity thresholds remain distinct fictional 08.2 checks. Zero DC is conditional on the rated/reverified DC block, never on arithmetic attenuation alone.
instrument	SYN-SA-A / SIM-003 / SIM-FW-1; fictional Gaussian front end, manual attenuation, optional idealized 20 dB preamp. Actual FPC documentation is orientation only, not a matching hardware claim.
settings	A: free-run [0,4) ms. B: supplied verified trigger yields [5,9) ms; analysis gate [0,30) ms. C: requested [0,30), dead [4,7), [14,17), [24,27) ms. Actual trigger threshold/slope/delay, pretrigger, holdoff, record depth, gate, dropped-frame indicators and IF bandwidth must accompany data.
calibration	Reverify path for burst/ramp bandwidth, DC/transient behavior and loss; verify trigger sensitivity using a known event and synchronized independent timing channel. Do not infer alignment merely from a common 10 MHz reference.
rawEvidence	SYN-SA-EVENTS-v1 schedule and SYN-SA-CAP-A/B/C-v1 immutable plans; preserve raw I/Q/envelope samples, dropped-frame/dead intervals, trigger state, gateway event log, full instrument setup and protection/calibration IDs. No synthetic outcome is represented as bench measurement.
processing	analyzer-settings-simulator/2.0; exact union/intersection/subtraction of half-open integer-μs intervals. A spectrogram is a separate STFT/time-gate analysis of actual samples; no timing raster is labelled a spectrum.
uncertainty	Timing quantization is 1 μs for the fixture. Actual trigger jitter, latency, clock alignment, event timestamp uncertainty, amplitude transient response and unobserved dead time are unresolved. Overlap arithmetic does not quantify a detection probability.
result	A: 4 ms live, 0/3 full captured. B: 4 ms live, 1 full, 2 missed, 1 ms event captured. C: 30 ms elapsed, 21 ms live, 9 ms dead, all 3 missed. Unknown timing phase yields unknown event outcomes.
inference	Longer elapsed observation can still miss every event. B succeeds here because its live interval overlaps a known event and trigger evidence is supplied. Real-world absence remains unproven.
unresolved	Actual ramp spectrum, analog bandwidth sufficiency, trigger sensitivity, gap-free behavior, timing uncertainty, overload and coupling mechanism need measured evidence.
next	Collect the verified-trigger record alongside an independent event log; repeat baseline/digital-activity controls without changing RF configuration. Use vector fixture evidence in planned 08.4 before attributing frequency-dependent path effects.
review	New waveform, firmware, gain state, cable movement, overload, unlock or loss of temperature stability invalidates the inference and requires review.

Engineering decision → record update

Hand the frequency-dependent external-path questions and raw evidence to 08.4 Vector Network Analysis, Calibration & Fixtures. Keep timing and estimator questions with the spectral method; a better fixture correction cannot reconstruct an event never acquired.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

01A corrected spur falls 20 dB when internal attenuation rises 10 dB. What can you infer?
Model answer
In the valid equal-tone cubic fixture, this is consistent with an internally generated IM3 product: mixer products fall 30 dB and input correction restores 10 dB. Main tones remain fixed. It is not proof of origin: changed noise masking, compression, automatic gain coupling or coherent external/internal cancellation can mimic a slope. Preserve A10/A20/A10 evidence and check each active stage’s reserve.
02The Gaussian RBW is 100 kHz. Can you subtract 50 dB from a noise reading to obtain density?
Model answer
Use the true ENBW, 106446.701943 Hz, so the correction is 50.271322101605 dB. The expected −99.728677898395 dBm noise reading becomes −150 dBm/Hz. Use a characterized noise estimator and include its applicable correction. A discrete CW tone must not receive the noise-marker bandwidth correction.
03Why do the same 1 and 9 mW samples give two different averages in dBm?
Model answer
Linear-power averaging gives 5 mW or 6.989700043360 dBm. Averaging their logarithms gives 4.771212547197 dBm. Sample-first is 0 dBm and bucket peak is 9.542425094393 dBm. Declare the domain and order of detection/video/trace averaging; a generic “average” label is incomplete.
04A 1 ms record is padded from 1024 to 4096 samples. Has resolution improved fourfold?
Model answer
The grid becomes 250 Hz instead of 1000 Hz. The acquired interval remains 1 ms and the periodic Hann ENBW remains 1500 Hz. Padding samples the same finite-record transform more densely; it neither acquires missing data nor narrows the window response. A longer acquired record is a different experiment.
05A 30 ms acquisition with 21 ms live time shows no event. Did the DUT stay quiet?
Model answer
No. Plan C’s dead intervals cover all three known 1 ms events exactly. Plan A also misses all events in 4 ms, whereas triggered B captures one in the same live duration. Unknown event phase or trigger sensitivity makes outcomes unknown. No independent-arrival probability or absence claim follows from elapsed time alone.
06Does −110 dBc/Hz phase noise or a 19.8396 kHz OBW establish compliance?
Model answer
Neither value supplies an applicable limit or procedure. Phase-noise attribution requires carrier/offset/ENBW/estimator and analyzer/source residual evidence; the result can be floor-limited. The OBW example is a synthetic equal-tail 99% PSD integral, not a standard waveform, necessary bandwidth, emissions mask or conformance verdict. Record the applicable method and limits separately.

References and further study

Primary sources consulted 2026-09-09. Diagrams, numerical fixtures, records and teaching thresholds are original Illustrative / Derived material. No measured DUT data or normative pass is supplied. Analytic levels are checked to 10⁻⁹ dB, powers/ENBW to 10⁻¹⁰ relative, complex DFT to 10⁻¹⁰ normalized error and Parseval to 10⁻⁹ relative; interval arithmetic is exact in integer μs. These tolerances describe numerical verification, not measurement uncertainty.

SA-BASICS · Rohde & Schwarz · Paul Denisowski. Understanding basic spectrum analyzer operation. Living educational page; no revision date displayed. Consulted: Center/span, reference level, RBW and VBW. Qualitative orientation; actual coupling and settling depend on the instrument.
DYNAMIC · Rohde & Schwarz · Paul Denisowski. Understanding dynamic range. Living educational page; no revision date displayed. Consulted: Noise, compression, spurs and phase-noise limits. Mechanisms only. This lesson’s intercepts, floors and ratings are fictional.
1MA201 · Rohde & Schwarz · Detlev Liebl. Measuring with Modern Spectrum Analyzers. Educational Note 1MA201_09e, February 2013 (cover). Consulted: §2.3.3–2.3.5, pp.18–24: tuning, IF processing, bandwidth, envelope/video. Conceptual basis for original diagrams and the Gaussian teaching model; no vendor sweep-time prediction.
FPC · Rohde & Schwarz. R&S FPC User Manual. 1178.4130.02, version 13, ©2025; firmware 1.90 and later. Consulted: §15.2.1 channel power; §15.2.6 OBW; §15.5 bandwidth; §15.6.3 sweep type; §15.7 trigger; §15.8.1–2 trace/detector. Named FPC1000/FPC1500 implementation. B22 preamp and K55 advanced measurements are options. Read installed firmware/options and current specifications; synthetic controls are not FPC emulation.
PERIODOGRAM · SciPy. scipy.signal.periodogram. Online API documentation, version 1.18.0 displayed at access. Consulted: Parameters scaling/return_onesided; Notes, density-to-spectrum normalization. Complex signals use two-sided output; the window sums determine the density/spectrum ratio.
HANN · SciPy. scipy.signal.windows.hann. Online API documentation, version 1.18.0 displayed at access. Consulted: sym parameter and Notes. Periodic (sym=False) spectral window distinguished from symmetric filter-design window.
CHANNEL · Rohde & Schwarz · Paul Denisowski. Understanding channel power measurements. Living educational page; no revision date displayed. Consulted: Channel definition; sensor, zero-span and integrated-bandwidth methods. Method choice and power-domain integration; the original piecewise PSD is not a standard waveform.
PHASE · Rohde & Schwarz. Measuring phase noise. Living educational page; no revision date displayed. Consulted: Direct spectrum method and phase-noise analyzer cross-correlation. SSB offset/carrier comparison and reduction of uncorrelated instrument contributions; no universal floor removal.
SM328 · ITU-R. Recommendation SM.328-12: Spectra and bandwidth of emissions. September 2025; approved 2025-09-01; catalogue status In force (Main), checked at access. Consulted: PDF recommends 1.1 reproducing RR 1.152–1.153; equal-tail occupied-bandwidth definition. Terminology only. Necessary bandwidth, OBW and an applicable emissions limit are different. No regulatory decision is supplied.

Revisit noise, time/frequency representations, blockers and headroom, and measurement uncertainty for the underlying models.

Spectrum &Signal Analysis

A disappearing spur can indict the analyzer

Follow the signal through the instrument

Allocate level and dynamic range at each plane

RBW selects frequency and collects noise

Detection and averaging change the estimator

A record defines what can be observed

Integrate spectral quantities with consistent units

Bursts require time and frequency evidence

Separate close-in noise, spurs, and residual floors

Defend two different acquisition plans

Analyzer Settings Simulator

Missed burst · A

Method 1 · A close-in weak spur beside a strong carrier

Method 2 · A rare gateway-correlated ramp or digital spur

Two complete, immutable method records

Check your understanding

References and further study

Spectrum &
Signal Analysis