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name: matlab-analyze-spectrum description: > Analyze signal spectra in MATLAB using nonparametric and parametric estimators. Use when computing frequency content, PSD, power spectrum, spectral peaks, bandwidth, or streaming spectral analysis. Covers pspectrum, pwelch, periodogram, pmtm, pburg, pmusic, rootmusic, plomb, poctave, spectrumAnalyzer, dsp.SpectrumEstimator. TRIGGER: FFT, PSD, power spectrum, spectral analysis, frequency content, bandwidth measurement, spectral leakage, window selection, streaming spectrum, periodicity, resolve close frequencies, multitaper. DO NOT TRIGGER: filter design, spectrogram/time-frequency, audio features. license: https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md metadata: author: MathWorks version: "1.0"

Analyze Signal Spectra in MATLAB

Compute, visualize, and extract measurements from signal spectra using Signal Processing Toolbox. Choose the right spectral estimator, avoid common FFT pitfalls, and use built-in measurement functions instead of reinventing them.

When to Use

• Computing frequency content of a signal (FFT, periodogram, PSD, power spectrum)
• Estimating power spectral density (Welch, periodogram, parametric)
• Comparing frequency content of two signals (cross-spectrum, coherence)
• Finding spectral peaks (dominant frequencies, harmonics)
• Measuring bandwidth, band power, or occupied bandwidth
• Visualizing frequency-domain data
• Streaming (real-time, frame-by-frame) spectral analysis with spectrumAnalyzer, dsp.SpectrumEstimator, dsp.CrossSpectrumEstimator

When NOT to Use

• Designing or applying filters -- use matlab-design-digital-filter
• Time-frequency/spectrogram analysis (including spectrumAnalyzer spectrogram ViewType, STFT, reassignment, CWT) -- use the time-frequency analysis skill (TBD)
• Audio-specific features (MFCC, pitch, auditory models) -- use Audio Toolbox
• Control system frequency response (Bode, Nyquist) -- use Control System Toolbox

Workflow

1. Batch or streaming? -- Determine if data is already in workspace (batch) or arrives frame-by-frame (streaming). See below.
2. Preliminary analysis -- When user provides data, run diagnostics to inform technique selection (see below)
3. Pre-process -- Check for NaN/gaps (use plomb for non-uniform data). Apply detrend(x) only if DC/trend visibly distorts the spectrum
4. Choose output type -- PSD, power spectrum, amplitude spectrum, or octave bands (see below)
5. Choose estimator -- Use preliminary analysis results + Estimator Selection below
6. Compute spectrum -- Use the chosen function with explicit Fs (if available)
7. Visualize -- Plot with proper axis labels (Hz, dB or linear units)
8. Extract metrics -- Use findpeaks, bandpower, obw, powerbw. See references/peak-detection.md
9. Verify -- Parseval's theorem, known tone levels. See references/power-from-spectrum.md

Batch vs Streaming

Determine the processing mode before choosing tools:

| Indicator | Mode | Tools | |-----------|------|-------| | Entire signal in workspace (vector/matrix) | Batch | pwelch, pspectrum, periodogram, pburg, etc. | | Data arrives frame-by-frame (sensor, ADC, real-time loop) | Streaming | spectrumAnalyzer, dsp.SpectrumEstimator, dsp.CrossSpectrumEstimator | | Need live-updating spectrum display | Streaming | spectrumAnalyzer (ViewType: spectrum) | | Need spectrum values for real-time decisions | Streaming | dsp.SpectrumEstimator (returns numeric output each frame) |

If streaming: See references/streaming-spectral-analysis.md for System object APIs, properties, and patterns. DSP System Toolbox is required.

The rest of this skill covers batch processing. For streaming, the reference file provides full guidance including the batch-to-streaming mapping table.

Preliminary Data Analysis

When the user provides signal data (variable, file, or description), run diagnostic checks before recommending a technique. See references/preliminary-analysis.md for full code.

Quick checks (run in order — stop early if decisive):

1. Sampling type — Fs given → uniform. Time vector with small jitter (<5%) → pspectrum(x,t) (resamples internally). Large jitter or truly non-uniform → plomb
2. Data quality — NaN/Inf, DC offset, trend → preprocess first
3. Length — <128: parametric only. 128–1024: periodogram/pburg. >10k: pwelch preferred
4. Spectral character — Run periodogram (Hann), compute spectral flatness + peak count + strongest peak width:
   • Flatness >0.3 → wideband → pwelch (peaks are just noise fluctuations)
   • Flatness <0.1, strongest peak narrow (width < 10×df) → tonal → periodogram(...,'power') or rootmusic
   • Flatness <0.1, strongest peak wide (width ≥ 10×df) → wideband-structured (chirps, shaped bands) → pwelch + obw
   • Flatness 0.1–0.3, peaks present → mixed → pwelch + findpeaks
5. AR fitness — Fit AR models with arburg, track prediction error vs order. If error plateaus <10% at low order → pburg is strong candidate
6. Tone count — If tonal: count peaks with findpeaks, cross-check with eigenvalue drop. Known count + resolution-limited → rootmusic(x,2*nTones,Fs)

Report findings to the user before computing the spectrum:

Preliminary Analysis:
- Sampling: uniform at [Fs] Hz
- Duration: [X] s ([N] samples), resolution: [df] Hz
- Spectral character: [wideband/tonal/mixed]
- AR fit: [quality] (order [N], residual [X]%)
Recommendation: [estimator] because [justification]

Output Type Selection

| User's Goal | Output Type | Function / Option | |-------------|-------------|-------------------| | Compare to a standard or another signal (length-independent) | PSD (power/Hz) | pwelch (default), periodogram | | Read amplitude of a specific tone | Power spectrum → sqrt | pspectrum(x,Fs) (default); periodogram(x,w,N,Fs,'power') or pwelch(x,w,[],[],Fs,'power') for explicit control | | Measure total power in a band | PSD then integrate, or use bandpower | bandpower(x,Fs,[fLow fHigh]) | | Octave-band levels (acoustics, vibration) | Fractional-octave spectrum | poctave(x,Fs,'BandsPerOctave',3) | | Detect frequencies in nearly-uniform data (small jitter) | Power spectrum | pspectrum(x,t) — resamples internally | | Detect frequencies in non-uniform/gapped data | Lomb-Scargle | plomb(x,t) |

PSD vs Power Spectrum: PSD (power/Hz) is resolution-independent — broadband noise stays flat when you change parameters. Power spectrum (power/bin) is tone-friendly — peak height equals true tone power. Use PSD for noise characterization and specs (g²/Hz, dBm/Hz); use power spectrum for reading tone amplitudes. Convert: PS = PSD × RBW where RBW = enbw(win)*Fs/segLen.

Estimator Selection

Decision tree (simple → specialized):

1. Just want to see what frequencies are present? → pspectrum(x,Fs)
2. Need a smooth, low-variance PSD? → pwelch (favored for long signals — segment averaging reduces variance) or periodogram (short signal, cannot segment)
3. Need accurate tone amplitude from peaks? → periodogram(x,win,N,Fs,'power') then sqrt
4. Need octave-band levels (acoustics, vibration)? → poctave(x,Fs,'BandsPerOctave',3)
5. Comparing two signals at each frequency? → mscohere (related?) / cpsd (shared content + phase)
6. Data is nearly uniform (small jitter)? → pspectrum(x,t) (resamples internally). Truly non-uniform or large gaps? → plomb(x,t)
7. Need to resolve sinusoids closer than Fs/N? → rootmusic / pmusic (must know # of sinusoids)
8. Short data, want low-variance PSD without segmenting? → pmtm (multitaper — uses orthogonal DPSS tapers on full record; no AR assumption)
9. Short data, want smooth sidelobe-free PSD? → pburg (assumes signal is AR-like)

Quick reference table:

| Goal | Function | When to use | |------|----------|-------------| | Quick look at frequency content | pspectrum | Default -- good defaults, tune Leakage (0–1) for resolution vs sidelobes | | Single-sided amplitude spectrum | periodogram with 'power' | Need amplitude per bin | | PSD with low variance | pwelch | Long signals — averaging segments reduces variance; preferred when signal is long enough to segment | | PSD of short signal, low variance | pmtm | Multitaper — uses full record with orthogonal DPSS tapers; no segmentation needed | | PSD of short signal | periodogram | Too short to segment; high variance (single window) | | Resolve closely-spaced sinusoids | pmusic, rootmusic | Known # of sinusoids, super-resolution | | Smooth PSD of short AR-like data | pburg | No sidelobes; NOT for resolving tones |

Default: Start with pspectrum. Drop to pwelch/periodogram for explicit control. Never use manual FFT unless user explicitly asks — redirect to built-in functions.

pspectrum vs pwelch: pspectrum outputs power spectrum (Kaiser beta=20, ~76% overlap). pwelch defaults to PSD. They match within ~0.2 dB using equivalent parameters. See references/pspectrum-equivalence.md for exact mapping. Resolution control in pspectrum: Use FrequencyResolution (Hz) to set target resolution directly, or Leakage (0–1) to control the resolution/sidelobe trade-off indirectly. TimeResolution is spectrogram-only — do NOT use it for power spectrum. Leakage parameter: pspectrum(x,Fs,Leakage=L) where L ∈ [0,1] — 0 = minimum leakage (max sidelobe suppression, widest main lobe), 1 = maximum leakage (rectangular window, best resolution), default 0.5.

Nonparametric vs Parametric: Use nonparametric (FFT-based) when signal is long or spectral shape is unknown. Use parametric when data is short, signal matches an AR model, or you need super-resolution. See references/estimator-comparison.md for detailed trade-offs.

Window Selection

| Goal | Window | Why | |------|--------|-----| | General-purpose PSD | Hann | Good balance, 50% overlap optimal | | Detect weak tone near strong tone | Blackman-Harris or Kaiser (beta≥10) | Low sidelobes (-92 dB) | | Resolve two close frequencies | Hann or Kaiser (beta=5) | Narrow main lobe | | Accurate amplitude measurement | Flat Top | ~0.01 dB scalloping loss | | Tunable trade-off | Kaiser(N,beta) | Single parameter controls curve |

Key rule: Higher sidelobe suppression costs wider main lobe. Only suppress as much as dynamic range requires. See references/spectral-windows.md for ENBW values and overlap guidelines.

Key Functions

| Function | Purpose | |----------|---------| | pspectrum | Power spectrum with automatic defaults; Leakage parameter (0–1) controls resolution vs sidelobe suppression | | periodogram | PSD or power spectrum via single-window DFT | | pwelch | PSD via Welch's averaged periodogram | | pmtm | PSD via Thomson's multitaper method (DPSS/Slepian tapers) | | cpsd | Cross power spectral density | | mscohere | Magnitude-squared coherence (0 to 1) | | pburg / pyulear | AR PSD (Burg / Yule-Walker) | | pmusic / peig | Pseudospectrum (MUSIC / eigenvector) | | rootmusic | Frequency estimation via root-MUSIC | | findpeaks | Locate spectral peaks | | refinepeaks | Sub-bin peak frequency/amplitude refinement (use after findpeaks) | | bandpower | Power in a frequency band | | obw / powerbw | Occupied bandwidth / 3-dB power bandwidth | | meanfreq / medfreq | Mean / median frequency of spectrum | | sfdr | Spurious free dynamic range | | toi | Third-order intercept point (two-tone intermodulation) | | spectralFlatness | Spectral flatness (0=tonal, 1=white noise) | | spectralCrest | Spectral peak-to-mean ratio | | spectralKurtosis | Spectral kurtosis (transient/non-stationarity detection) | | poctave | Fractional-octave spectrum | | plomb | Lomb-Scargle periodogram (non-unif