Matlab Analyze Time Frequency

Time-Frequency Analysis in MATLAB

Analyze how frequency content evolves over time using STFT, CWT, synchrosqueezing,

reassignment, cross-signal methods, and data-adaptive decomposition.

> Agent directive: Consult the reference guides in references/ before answering.

> Each guide covers a specific domain with syntax, gotchas, and common mistakes.

When To Use

• Analyzing how frequency content evolves over time (spectrogram, scalogram)
• Choosing between STFT, CWT, synchrosqueezing, reassignment, or EMD/VMD
• Extracting and reconstructing individual signal components from a TF representation
• Computing time-varying coherence or cross-spectrum between two signals
• Decomposing signals into additive time-domain components (wavelet MRA, EMD, VMD)
• Estimating instantaneous frequency or Hilbert spectrum

When Not To Use

• Designing or applying classical FIR/IIR filters — use matlab-design-digital-filter
• Extracting scalar features for ML classification — use matlab-extract-signal-features
• Signal preprocessing (resampling, detrending, gap filling) — use matlab-prepare-signal-data
• Quadratic/bilinear TFDs (Wigner-Ville) — not supported in MATLAB toolboxes
• Audio-specific representations (mel spectrogram, MFCC) — use Audio Toolbox

Method Selection

Choose the analysis method based on the user's goal and signal characteristics:

| Goal | Method | Guide |

|------|--------|-------|

| Interactive TF exploration (spectrogram + scalogram) | signalAnalyzer | — |

| General TF visualization (uniform freq resolution) | stft, spectrogram, pspectrum | references/stft-guide.md |

| TF visualization (multi-resolution, constant-Q) | cwt, cwtfilterbank | references/cwt-guide.md |

| Sharpest TF picture (non-invertible) | spectrogram("reassigned"), pspectrum(Reassigned=true) | references/reassignment-guide.md |

| Remove specific TF regions (mask-based filtering) | tffilt with binary mask | references/stft-guide.md |

| Mode extraction + reconstruction (STFT domain) | fsst → tfridge → ifsst | references/reassignment-guide.md |

| Mode extraction + reconstruction (CWT domain) | wsst → wsstridge → iwsst | references/reassignment-guide.md |

| Signal reconstruction from CWT | icwt (exact or approximate) | references/cwt-guide.md |

| Additive decomposition (octave bands) | modwt + modwtmra | references/multiresolution-guide.md |

| Additive decomposition (uniform bands) | modwptdetails | references/multiresolution-guide.md |

| Adaptive decomposition (unknown components) | emd | references/multiresolution-guide.md |

| Adaptive decomposition (known mode count) | vmd | references/multiresolution-guide.md |

| Hilbert spectrum / instantaneous frequency | hht, instfreq | references/multiresolution-guide.md |

| Time-varying coherence between two signals | wcoherence | references/cross-analysis-guide.md |

| Cross spectrogram between two signals | xspectrogram | references/cross-analysis-guide.md |

| Global coherence (no time axis) | mscohere, cpsd | references/cross-analysis-guide.md |

For detailed decision logic, see references/method-selection-guide.md.

Quick Decision Tree

What is the primary goal?
│
├── Interactive exploration (adjust parameters, compare views)
│   └── signalAnalyzer — supports spectrogram + scalogram (CWT) side by side
│
├── Visualize one signal's TF content
│   ├── Need uniform frequency resolution? → stft / spectrogram / pspectrum
│   ├── Need multi-resolution (better low-freq)? → cwt
│   └── Need sharpest picture (no reconstruction)? → spectrogram("reassigned")
│
├── Remove unwanted content visible in spectrogram
│   └── Define binary mask over TF plane → tffilt (Gabor domain)
│
├── Extract and reconstruct individual components
│   ├── From TF representation (invertible)?
│   │   ├── STFT domain → fsst → tfridge → ifsst
│   │   └── CWT domain → wsst → wsstridge → iwsst
│   ├── Additive time-domain components?
│   │   ├── Octave bands → modwt + modwtmra
│   │   ├── Uniform bands → modwptdetails
│   │   └── Data-adaptive → emd or vmd
│   └── From CWT directly? → icwt (see references/cwt-guide.md)
│
├── Compare two signals
│   ├── Time-varying coherence? → wcoherence
│   ├── Time-varying cross-spectrum? → xspectrogram
│   └── Global relationship? → mscohere / cpsd
│
└── Estimate instantaneous frequency
    ├── Single monocomponent signal? → instfreq(x, fs)
    ├── Multicomponent (want per-mode IF)? → emd → instfreq(imf, fs)
    └── Multicomponent (want single average)? → instfreq(x, fs, Method="tfmoment")

Critical Rules

• stft has no reassignment option. Use fsst for invertible synchrosqueezing or spectrogram("reassigned") for non-invertible visualization.

• wsstridge argument order differs from tfridge:
• wsstridge(sst, penalty, f, ...) — penalty is 2nd positional arg
• tfridge(tfm, f, penalty, ...) — penalty is 3rd positional arg

• wsst subtracts the signal mean internally. iwsst does NOT restore it. Add mean(x) back manually if DC matters.

• ifsst is machine-precision; iwsst is approximate (Morlet single-integral formula).

• xspectrogram first output is real (cross-spectrogram magnitude). For phase, use the 4th output P. This differs from spectrogram whose first output is complex STFT.

• wcoherence has no Parent option. For App Designer, compute outputs and plot manually.

• wcoherence phase arrows show the phase lag of Y relative to X:
• ↑ = Y lags X by π/2
• ↓ = Y leads X by π/2
• → = in-phase
• ← = anti-phase

PhaseDisplayThreshold (default 0.5) is plot-only — it controls which arrows are drawn but has no effect on returned numeric outputs.

• hht takes IMFs, not raw signal. Always decompose first: imf = emd(x); hht(imf, fs).

• instfreq Hilbert method is meaningless for multicomponent signals. Decompose first, or use Method="tfmoment" for a single average curve.

10. Synchrosqueezing is precision-sensitive. Use double-precision data with fsst/wsst for reproducible results across MATLAB, codegen, and GPU.

Signal Assessment Workflow

When the user provides a signal and asks "what should I use?", run the assessment script then apply agent-side interpretation:

Step 1: Run MATLAB assessment

report = assessSignalForTF(x, fs);
disp(report)
disp(report.recommendations)

The script returns: signal length, occupied bandwidth, number of spectral peaks (with frequencies), nonstationarity indicator, DC content, precision, and auto-generated recommendations.

Step 2: Agent-side interpretation (combine script output with user goals)

| User Goal | Key Report Fields | Recommendation Logic |

|-----------|-------------------|---------------------|

| "Explore / I'm not sure what I need" | — | Suggest signalAnalyzer for interactive exploration (spectrogram + scalogram views, adjustable parameters) |

| "Visualize frequency content over time" | likelyNonstationary, fractionalBandwidth | If wideband (>2 octaves): cwt. If narrowband or uniform resolution needed: stft/spectrogram |

| "Separate/extract components" | numSpectralPeaks, peakFrequenciesHz | 2–3 peaks: synchrosqueezing (fsst/wsst). Many peaks: emd/vmd. Closely-spaced: modwptdetails or fsst |

| "Reconstruct after filtering" | hasDC, precision | fsst/ifsst for exact. wsst/iwsst for CWT-domain (warn about mean). icwt for CWT bandpass |

| "Compare two signals" | (run on both) | wcoherence for coherence. xspectrogram for cross-spectrum |

| "Detect transients/events" | signalLength, occupiedBandHz | cwt with low TimeBandwidth. Or short-window stft |

Step 3: Refine with follow-up questions if ambiguous

• "Do you need to reconstruct the signal, or just visualize?"
• "Do you need uniform frequency resolution, or is multi-resolution acceptable?"
• "Are you comparing this signal to another?"

Reference Guides

| File | Coverage |

|------|----------|

| references/stft-guide.md | stft/istft, spectrogram, pspectrum, stftmag2sig, length preservation, COLA |

| references/cwt-guide.md | cwt, cwtfilterbank, icwt, dlicwt/icwtLayer, boundary, constant-Q |

| references/reassignment-guide.md | fsst/ifsst, wsst/iwsst, spectrogram("reassigned"), pspectrum(Reassigned=true), ridge extraction, penalty |

| references/cross-analysis-guide.md | wcoherence, xspectrogram, cpsd, mscohere, phase arrows, unsmoothed cross-spectrum |

| references/multiresolution-guide.md | modwt/modwtmra, modwpt/modwptdetails, emd, vmd, hht, instfreq, instbw |

| references/method-selection-guide.md | Decision logic for choosing among all methods |

Toolbox Requirements

| Toolbox | Functions |

|---------|-----------|

| Signal Processing | stft, istft, spectrogram, pspectrum, fsst, ifsst, tfridge, xspectrogram, instfreq, instbw, stftmag2sig, cpsd, mscohere |

| Wavelet | cwt, cwtfilterbank, icwt, wsst, iwsst, wsstridge, wcoherence, modwt, modwtmra, modwpt, modwptdetails, emd, vmd, hht, tffilt, dgt |

| Function | Available From | Note |

|----------|---------------|------|

| tffilt | R2025a | TF mask-based filtering; all other functions available in R2024b |

Documentation References

| Topic | Link |

|-------|------|

| Time-frequency gallery | https://www.mathworks.com/help/signal/time-frequency-analysis.html |

| Wavelet time-frequency | https://www.mathworks.com/help/wavelet/time-frequency-analysis.html |

| CWT reference | https://www.mathworks.com/help/wavelet/ref/cwt.html |

| STFT reference | https://www.mathworks.com/help/signal/ref/stft.html |

| Synchrosqueezing example | https://www.mathworks.com/help/wavelet/ug/time-frequency-reassignment-and-mode-extraction-with-synchrosqueezing.html |

| Wavelet coherence example | https://www.mathworks.com/help/wavelet/ug/compare-time-frequency-content-in-signals-with-wavelet-coherence.html |

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