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.

Apps

Signal Analyzer	Visualize and compare multiple signals and spectra
Signal Labeler	Label signal attributes, regions, and points of interest, and extract features

Functions

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Estimators

`fsst`	Fourier synchrosqueezed transform
`ifsst`	Inverse Fourier synchrosqueezed transform
`instbw`	Estimate instantaneous bandwidth
`instfreq`	Estimate instantaneous frequency
`kurtogram`	Visualize spectral kurtosis
`pkurtosis`	Spectral kurtosis from signal or spectrogram
`pentropy`	Spectral entropy of signal
`pspectrum`	Analyze signals in the frequency and time-frequency domains
`spectrogram`	Spectrogram using short-time Fourier transform
`xspectrogram`	Cross-spectrogram using short-time Fourier transforms
`stft`	Short-time Fourier transform
`dlstft`	Deep learning short-time Fourier transform
`stftLayer`	Short-time Fourier transform layer
`stftmag2sig`	Signal reconstruction from STFT magnitude
`iscola`	Determine whether window-overlap combination is COLA compliant
`istft`	Inverse short-time Fourier transform
`tfridge`	Time-frequency ridges
`wvd`	Wigner-Ville distribution and smoothed pseudo Wigner-Ville distribution
`xwvd`	Cross Wigner-Ville distribution and cross smoothed pseudo Wigner-Ville distribution

Data-Adaptive Methods

`emd`	Empirical mode decomposition
`vmd`	Variational mode decomposition
`hht`	Hilbert-Huang transform

Topics

Time-Frequency Estimation

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.
FFT-Based Time-Frequency Analysis
Display the spectrogram and persistence spectrum of a linear FM signal.
Instantaneous Frequency of Complex Chirp
Compute the instantaneous frequency of a signal using the Fourier synchrosqueezed transform.
Detect Closely Spaced Sinusoids with the Fourier Synchrosqueezed Transform
Determine how separate in frequency two sinusoids must be for the Fourier synchrosqueezed transform to resolve them.

Time-Frequency Applications

Practical Introduction to Continuous Wavelet Analysis (Wavelet Toolbox)
Perform and interpret continuous wavelet analysis.
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.
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).

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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