matlab-analyze-time-frequency-content

Use STFT (stft, spectrogram) when you need uniform frequency resolution or must resolve closely-spaced high-frequency tones. Use CWT (cwt) for multi-resolution analysis of signals with transients or wideband content, since its constant-Q property gives better time resolution at high frequencies.

Use synchrosqueezing: fsst followed by tfridge and ifsst in the STFT domain gives machine-precision reconstruction, or wsst with wsstridge and iwsst in the CWT domain for approximate reconstruction. Note that wsst subtracts the signal mean and iwsst does not restore it.

wcoherence computes time-varying magnitude-squared coherence between two signals using wavelets, while xspectrogram computes the time-varying cross-spectrum using the STFT with uniform frequency resolution. For phase information from xspectrogram, use its fourth output since the first output is real magnitude only.

The ratio (Nx - L) / (M - L) must be an integer for istft to preserve length, where Nx is signal length, L is overlap, and M is window length. Adjust the window or overlap parameters to satisfy this condition, and verify the COLA constraint with iscola.

Use EMD for exploratory analysis when the number of components is unknown, since it is fully adaptive but may return fewer modes than MaxNumIMF. Use VMD when you know the exact number of narrowband components, as NumIMFs is an exact count and the optimization separates modes cleanly.

STFT, spectrogram, fsst, and xspectrogram require Signal Processing Toolbox, while cwt, wsst, wcoherence, modwt, emd, vmd, and hht require Wavelet Toolbox. Most functions are available from R2024b, except tffilt which requires R2025a.