Time-Frequency Analysis

Spectrogram, synchrosqueezing, reassignment, Wigner-Ville, time-frequency marginals, data-adaptive methods

Signal Processing Toolbox™ provides functions and apps that enable you to visualize and compare time-frequency content of nonstationary signals. Compute the short-time Fourier transform and its inverse. Obtain sharp spectral estimates using reassignment or Fourier synchrosqueezing. Plot cross-spectrograms, Wigner-Ville distributions, and persistence spectra. Extract and track time-frequency ridges. Estimate instantaneous frequency, instantaneous bandwidth, spectral kurtosis, and spectral entropy. Perform data-adaptive time-frequency analysis using empirical or variational mode decomposition and the Hilbert-Huang transform. Explore other time-frequency representations and analysis methods using the functions and apps provided by Wavelet Toolbox™.

Apps

Signal Analyzer	Visualize and compare multiple signals and spectra
Signal Labeler	Label signal attributes, regions, and points of interest, and extract features
Signal Multiresolution Analyzer	Decompose signals into time-aligned components
Wavelet Time-Frequency Analyzer	Visualize scalogram of signals (Since R2022a)

Functions

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Transforms

`fsst`	Fourier synchrosqueezed transform
`ifsst`	Inverse Fourier synchrosqueezed transform
`stft`	Short-time Fourier transform
`istft`	Inverse short-time Fourier transform
`dlstft`	Deep learning short-time Fourier transform (Since R2021a)
`dlistft`	Deep learning inverse short-time Fourier transform (Since R2024a)
`stftLayer`	Short-time Fourier transform layer (Since R2021b)
`istftLayer`	Inverse short-time Fourier transform layer (Since R2024a)
`stftmag2sig`	Signal reconstruction from STFT magnitude (Since R2020b)
`iscola`	Determine whether window-overlap combination is COLA compliant
`spectrogram`	Spectrogram using short-time Fourier transform
`xspectrogram`	Cross-spectrogram using short-time Fourier transforms
`pspectrum`	Analyze signals in the frequency and time-frequency domains
`kurtogram`	Visualize spectral kurtosis
`wvd`	Wigner-Ville distribution and smoothed pseudo Wigner-Ville distribution
`xwvd`	Cross Wigner-Ville distribution and cross smoothed pseudo Wigner-Ville distribution

Spectral Descriptors

`instbw`	Estimate instantaneous bandwidth (Since R2021a)
`instfreq`	Estimate instantaneous frequency
`spectralCrest`	Spectral crest for signals and spectrograms
`spectralEntropy`	Spectral entropy for signals and spectrograms
`spectralFlatness`	Spectral flatness for signals and spectrograms
`spectralKurtosis`	Spectral kurtosis for signals and spectrograms
`spectralSkewness`	Spectral skewness for signals and spectrograms
`tfridge`	Time-frequency ridges

Data-Adaptive Methods

`emd`	Empirical mode decomposition
`ewt`	Empirical wavelet transform (Since R2020b)
`vmd`	Variational mode decomposition (Since R2020a)
`hht`	Hilbert-Huang transform

Time-Frequency Analysis with Wavelets

`cqt`	Constant-Q nonstationary Gabor transform
`cwt`	Continuous 1-D wavelet transform
`modwpt`	Maximal overlap discrete wavelet packet transform
`modwt`	Maximal overlap discrete wavelet transform
`tqwt`	Tunable Q-factor wavelet transform (Since R2021b)
`waveletScattering`	Wavelet time scattering
`wcoherence`	Wavelet coherence and cross-spectrum
`wsst`	Wavelet synchrosqueezed transform

Topics

Spectrogram Computation with Signal Processing Toolbox
Compute and display spectrograms of signals using Signal Processing Toolbox functions.
Time-Frequency Gallery
Examine the features and limitations of the time-frequency analysis functions provided by Signal Processing Toolbox.
Practical Introduction to Time-Frequency Analysis Using the Continuous Wavelet Transform (Wavelet Toolbox)
Perform and interpret time-frequency analysis of signals using the continuous wavelet transform. (Since R2020a)
Practical Introduction to Multiresolution Analysis (Wavelet Toolbox)
Perform and interpret basic signal multiresolution analysis (MRA). (Since R2020a)
Wavelet Packet Harmonic Interference Removal (Wavelet Toolbox)
Use wavelet packets to remove harmonic interference from an electrocardiogram (ECG) signal. (Since R2021b)
Pedestrian and Bicyclist Classification Using Deep Learning (Radar Toolbox)
Classify pedestrians and bicyclists based on their micro-Doppler characteristics using deep learning and time-frequency analysis. (Since R2021a)
Radar and Communications Waveform Classification Using Deep Learning (Phased Array System Toolbox)
Classify radar and communications waveforms using the Wigner-Ville distribution (WVD) and a deep convolutional neural network (CNN).
Spectral Descriptors (Audio Toolbox)
Overview and applications of spectral descriptors.

Related Information

Time-Frequency Analysis (Wavelet Toolbox)

Featured Examples

Classify ECG Signals Using Long Short-Term Memory Networks

Classify heartbeat electrocardiogram data using deep learning and signal processing.

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Waveform Segmentation Using Deep Learning

Segment human electrocardiogram signals using time-frequency analysis and deep learning.

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Spoken Digit Recognition with Custom Log Spectrogram Layer and Deep Learning

Classify spoken digits using a deep convolutional neural network and a custom spectrogram layer.

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Signal Recovery with Differentiable Scalograms and Spectrograms

Use differentiable time-frequency transforms to recover a time-domain signal without the need for phase information or transform inversion.

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Practical Introduction to Time-Frequency Analysis

Perform and interpret basic time-frequency signal analysis of nonstationary signals.

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Cross-Spectrogram of Complex Signals

Highlight the regions where two signals share frequency content.

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Find Interference Using Persistence Spectrum

Use the persistence spectrum in Signal Analyzer app to detect and analyze brief events.

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Find and Track Ridges Using Reassigned Spectrogram

Use the reassigned spectrogram in Signal Analyzer to sharpen the time and frequency localization of spectrograms.

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