# signalTimeFrequencyFeatureExtractor

## Description

Use a `signalTimeFrequencyFeatureExtractor`

object to extract time-frequency-domain
features from a signal. You can use the extracted features to train a machine learning model
or a deep learning network.

## Creation

### Syntax

### Description

creates a `sFE`

= signalTimeFrequencyFeatureExtractor`signalTimeFrequencyFeatureExtractor`

object with default property values.

sets property values to the `sFE`

= signalTimeFrequencyFeatureExtractor(`Name=Value`

)`signalTimeFrequencyFeatureExtractor`

object. For example,
`signalTimeFrequencyFeatureExtractor(FrameSize=30,FrameOverlapLength=6)`

creates a `signalTimeFrequencyFeatureExtractor`

object that partitions a signal into overlapping
30-sample frames to extract time-frequency features from each frame.

## Properties

### Main Properties

`FrameSize`

— Number of samples per frame

positive integer

Number of samples per frame, specified as a positive integer. The
object divides the signal into frames of the specified length
and extracts features for each frame. If you do not specify
`FrameSize`

, or if you specify
`FrameSize`

as empty, the object
extracts features for the whole signal.

**Data Types: **`single`

| `double`

`FrameRate`

— Number of samples between start of frames

positive integer

Number of samples between the start of frames, specified as a positive integer. The frame rate
determines the distance in samples between the starting points
of frames. If you specify `FrameRate`

, then
you must also specify `FrameSize`

. If you do
not specify `FrameRate`

or
`FrameOverlapLength`

, then the
object assumes `FrameRate`

to be equal to
`FrameSize`

. You cannot specify
`FrameRate`

and
`FrameOverlapLength`

simultaneously.

**Data Types: **`single`

| `double`

`FrameOverlapLength`

— Number of overlapping samples between consecutive frames

positive integer

Number of overlapping samples between consecutive frames, specified as a positive
integer. `FrameOverlapLength`

must be less than or equal to the frame
size. If you specify `FrameOverlapLength`

, then you must also specify
`FrameSize`

. You cannot specify
`FrameOverlapLength`

and `FrameRate`

simultaneously.

**Data Types: **`single`

| `double`

`SampleRate`

— Sample rate

`[]`

(default) | positive scalar

Input sample rate, specified as a positive scalar in hertz.

If you do not specify `SampleRate`

, the `extract`

function of the object assumes the signal
sampling rate as 2π Hz.

**Data Types: **`single`

| `double`

`FeatureFormat`

— Format of generated features

`"matrix"`

(default) | `"table"`

Format of the features generated by the `extract`

function, specified as one of these:

`"matrix"`

— Columns correspond to feature values.`"table"`

— Each table variable corresponds to a feature value.

**Data Types: **`char`

| `string`

`IncompleteFrameRule`

— Rule to handle incomplete frames

`"drop"`

(default) | `"zeropad"`

Rule to handle incomplete frames, specified as one of these:

`"drop"`

— Drop the incomplete frame and do not use it to compute features.`"zeropad"`

— Zero-pad the incomplete frame and use it to compute features.

This rule applies when the current frame size is less than the specified
`FrameSize`

property.

**Data Types: **`char`

| `string`

`Transform`

— Time-frequency analysis method

`"spectrogram"`

(default) | `"synchrosqueezedspectrogram"`

| `"emd"`

| `"vmd"`

| `"scalogram"`

| `"synchrosqueezedscalogram"`

| `"wavelet"`

| `"waveletpacket"`

Time-frequency analysis method used to extract signal features from, specified as:

`"spectrogram"`

— Short-time Fourier transform (`stft`

)`"synchrosqueezedspectrogram"`

— Fourier synchrosqueezed transform (`fsst`

)`"emd"`

— Empirical mode decomposition (`emd`

)`"vmd"`

— Variational mode decomposition (`vmd`

)`"scalogram"`

— Continuous wavelet transform (`cwt`

(Wavelet Toolbox)) magnitude`"synchrosqueezedscalogram"`

— Wavelet synchrosqueezed transform (`wsst`

(Wavelet Toolbox)) magnitude`"wavelet"`

— Maximal overlap discrete wavelet transform (`modwt`

(Wavelet Toolbox))`"waveletpacket"`

— Maximal overlap discrete wavelet packet transform (`modwpt`

(Wavelet Toolbox))

See Time-Frequency Gallery for more information on time-frequency analysis methods.

Depending on the value you set in `Transform`

, you can extract
the following time-frequency features.

Features to Extract | Supported Values for
`Transform` | ||||
---|---|---|---|---|---|

`"spectrogram"` ,`"synchrosqueezedspectrogram"` ,`"synchrosqueezedscalogram"` | `"emd"` | `"vmd"` | `"scalogram"` | `"wavelet"` ,`"waveletpacket"` | |

`SpectralKurtosis` | ✓ | ||||

`SpectralSkewness` | ✓ | ||||

`SpectralCrest` | ✓ | ||||

`SpectralFlatness` | ✓ | ||||

`SpectralEntropy` | ✓ | ||||

`TFRidges` | ✓ | ||||

`InstantaneousBandwidth` | ✓ | ||||

`InstantaneousFrequency` | ✓ | ✓ | ✓ | ✓ | |

`InstantaneousEnergy` | ✓ | ✓ | ✓ | ||

`MeanEnvelopeEnergy` | ✓ | ||||

`WaveletEntropy` | ✓ | ||||

`TimeSpectrum` | ✓ | ||||

`ScaleSpectrum` | ✓ |

**Note**

You must have a Wavelet Toolbox™ license to specify

`Transform`

as`"scalogram"`

,`"synchrosqueezedscalogram"`

,`"wavelet"`

, or`"waveletpacket"`

.You cannot specify

`FrameSize`

,`FrameRate`

, or`FrameOverlapLength`

when`Transform`

is`"emd"`

or`"vmd"`

.

**Data Types: **`char`

| `string`

`ScalarizationMethod`

— Methods to convert feature vectors to scalar values

`timeFrequencyScalarFeatureOptions`

object

Methods to convert feature vectors to scalar values, specified as a `timeFrequencyScalarFeatureOptions`

object.

You can specify methods to extract scalar feature values from the Features to Extract. Specify
scalarization methods to a feature extractor object by using the
`ScalarizationMethod`

name-value argument or the `setScalarizationMethods`

function.

If you specify

`ScalarizationMethod`

, the`signalTimeFrequencyFeatureExtractor`

object returns the corresponding scalar values for each feature vector.To convert a feature vector to scalar feature values:

You must enable the feature for extraction by setting the feature name in the

`signalTimeFrequencyFeatureExtractor`

object to`true`

.You must specify the desired scalarization methods for each feature name using a cell array of character vectors or a string array and store the information in a

`timeFrequencyScalarFeatureOptions`

object.

After that, the

`extract`

function:Extracts the vectors corresponding to each enabled feature.

Takes the list of scalarization methods compiled by the object and for each method computes the corresponding scalar value.

Concatenates the vector features and the scalar features.

If you do not specify

`ScalarizationMethod`

, the`signalTimeFrequencyFeatureExtractor`

object does not perform any scalarization.

For more information about scalarization methods, see Scalarization Methods for Signal Features in Time-Frequency Domain.

### Features to Extract

You can enable signal features using name-value arguments from the time-frequency signal
representation that you specify in `Transform`

.

**Example: **`signalTimeFrequencyFeatureExtractor(Transform="emd",InstantaneousEnergy=true,MeanEnvelopeEnergy=true)`

`SpectralKurtosis`

— Option to extract spectral kurtosis

`false`

(default) | `true`

Option to extract the spectral kurtosis of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `SpectralKurtosis`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.The

`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the spectral kurtosis feature, see `spectralKurtosis`

.

**Data Types: **`logical`

`SpectralSkewness`

— Option to extract spectral skewness

`false`

(default) | `true`

Option to extract the spectral skewness of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `SpectralSkewness`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.The

`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the spectral skewness feature, see `spectralSkewness`

.

**Data Types: **`logical`

`SpectralCrest`

— Option to extract spectral crest

`false`

(default) | `true`

Option to extract the spectral crest of the time-frequency signal representation,
specified as `true`

or `false`

.

If you specify `SpectralCrest`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.The

`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the spectral crest feature, see `spectralCrest`

.

**Data Types: **`logical`

`SpectralFlatness`

— Option to extract spectral flatness

`false`

(default) | `true`

Option to extract the spectral flatness of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `SpectralFlatness`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the spectral flatness feature, see `spectralFlatness`

.

**Data Types: **`logical`

`SpectralEntropy`

— Option to extract spectral entropy

`false`

(default) | `true`

Option to extract the spectral entropy of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `SpectralEntropy`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the spectral entropy feature, see `spectralEntropy`

.

**Data Types: **`logical`

`TFRidges`

— Option to extract time-frequency ridges

`false`

(default) | `true`

Option to extract the time-frequency ridges of the time-frequency signal
representation, specified as `true`

or `false`

.

If you specify `TFRidges`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the time-frequency ridge feature, see `tfridge`

.

**Data Types: **`logical`

`InstantaneousBandwidth`

— Option to extract instantaneous bandwidth

`false`

(default) | `true`

Option to extract the instantaneous bandwidth of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `InstantaneousBandwidth`

as
`true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the instantaneous bandwidth feature, see `instbw`

.

**Data Types: **`logical`

`InstantaneousFrequency`

— Option to extract instantaneous frequency

`false`

(default) | `true`

Option to extract the instantaneous frequency of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `InstantaneousFrequency`

as
`true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the instantaneous frequency feature, see `instfreq`

or `hht`

.

**Data Types: **`logical`

`InstantaneousEnergy`

— Option to extract instantaneous energy

`false`

(default) | `true`

Option to extract the instantaneous energy of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `InstantaneousEnergy`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the instantaneous energy feature, see `hht`

.

**Data Types: **`logical`

`MeanEnvelopeEnergy`

— Option to extract mean envelope energy

`false`

(default) | `true`

Option to extract the mean energy of the upper and lower envelopes for each
intrinsic mode function (IMF) of the time-frequency signal representation, specified
as `true`

or `false`

.

If you specify `MeanEnvelopeEnergy`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the mean-envelope energy feature, see `emd`

.

**Data Types: **`logical`

`WaveletEntropy`

— Option to extract wavelet entropy

`false`

(default) | `true`

Option to extract the wavelet entropy of the time-frequency signal representation,
specified as `true`

or `false`

.

If you specify `WaveletEntropy`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the wavelet entropy feature, see `wentropy`

(Wavelet Toolbox).

**Data Types: **`logical`

`TimeSpectrum`

— Option to extract time-averaged wavelet spectrum

`false`

(default) | `true`

Option to extract the time-averaged wavelet spectrum of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `TimeSpectrum`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the time spectrum feature, see `timeSpectrum`

(Wavelet Toolbox).

**Data Types: **`logical`

`ScaleSpectrum`

— Option to extract scale-averaged wavelet spectrum

`false`

(default) | `true`

Option to extract the scale-averaged wavelet spectrum of the time-frequency signal
representation, specified as `true`

or
`false`

.

If you specify `ScaleSpectrum`

as `true`

:

The

`signalTimeFrequencyFeatureExtractor`

object enables this feature for extraction.`extract`

object function extracts this feature and concatenates it with all the other features that you enable in the`signalTimeFrequencyFeatureExtractor`

object.

For more information about the scale spectrum feature, see `scaleSpectrum`

(Wavelet Toolbox).

**Data Types: **`logical`

## Object Functions

`extract` | Extract time-domain, frequency-domain, or time-frequency-domain features |

`generateMATLABFunction` | Create MATLAB function compatible with C/C++ code generation |

`getExtractorParameters` | Get current parameter values of feature extractor object |

`getScalarizationMethods` | Get current scalarization methods of feature extractor object |

`setExtractorParameters` | Set nondefault parameter values for feature extractor object |

`setScalarizationMethods` | Set scalarization methods for feature extractor object |

## Examples

### Extract Time-Frequency Features from Chirp Signal

Extract the spectral kurtosis and instantaneous frequency from the spectrogram of a quadratic-swept chirp signal.

Generate a chirp with quadratic instantaneous frequency deviation. The chirp is sampled at 2$\pi $ Hz for 60 seconds. The instantaneous frequency is 0.5 Hz at *t* = 0 and crosses 2 Hz at *t* = 60 seconds.

```
fs = 2*pi;
t = 0:1/fs:60;
x = chirp(t,0.5,60,2,"quadratic");
```

Create a `signalTimeFrequencyFeatureExtractor`

object and enable the `SpectralKurtosis`

and `InstantaneousFrequency`

time-frequency-domain features.

```
tfFE = signalTimeFrequencyFeatureExtractor( ...
SpectralKurtosis=true,InstantaneousFrequency=true)
```

tfFE = signalTimeFrequencyFeatureExtractor with properties: Properties FrameSize: [] FrameRate: [] SampleRate: [] IncompleteFrameRule: "drop" FeatureFormat: "matrix" Transform: "Spectrogram" ScalarizationMethod: [1x1 timeFrequencyScalarFeatureOptions] Enabled Features SpectralKurtosis, InstantaneousFrequency Disabled Features SpectralSkewness, SpectralCrest, SpectralFlatness, SpectralEntropy, TFRidges, InstantaneousBandwidth MeanEnvelopeEnergy, InstantaneousEnergy, WaveletEntropy, TimeSpectrum, ScaleSpectrum

Extract the features from the chirp signal. Reshape the result into the number of features extracted. Plot the features.

features = extract(tfFE,x); featuresRows = reshape(features,[],2); stackedplot(featuresRows,"*",... DisplayLabels=["Spectral Kurtosis" "Instantaneous Frequency"]) grid on

### Extract Time-Frequency Features from `signalDatastore`

Object

Set up a three-signal `signalDatastore`

object and a `signalTimeFrequencyFeatureExtractor`

object. Extract the spectral skewness and time-frequency ridges to the signals.

Create a `signalDatastore`

object with three oscillating signals sampled at 3000 Hz for 3 seconds.

Fs = 3000; t = 0:1/Fs:3; members = {chirp(t,300,t(end),800); ... 2*chirp(t,200,t(end),1000,"quadratic",[],"concave"); ... vco(sin(2*pi*t),[0.1 0.4]*Fs,Fs)}; sds = signalDatastore(members,SampleRate=Fs);

Create a `signalTimeFrequencyFeatureExtractor`

object defining a sample rate. Enable the spectral skewness and time-frequency ridges as features to extract.

```
tfFE = signalTimeFrequencyFeatureExtractor(SampleRate=Fs, ...
SpectralSkewness=true,TFRidges=true);
```

Set up the extractor parameters for a `signalTimeFrequencyFeatureExtractor`

object. Specify the range between `Fs/5`

and `Fs/2.5`

to extract the spectral skewness. Set the penalty parameter to zero to extract the time-frequency ridges.

setExtractorParameters(tfFE,"SpectralSkewness",Range=[Fs/5 Fs/2.5]); setExtractorParameters(tfFE,"TFRidges",Penalty=0);

Extract and plot the time-frequency features to all the signals from a `signalDatastore`

object.

tiledlayout flow signalID = 1; while hasdata(sds) [data,info] = read(sds); % Extract features and remove small values. [features,infofeatures] = extract(tfFE,data); features(abs(features)<1e-4)=0; % Plot the spectral skewness nexttile plot(features(infofeatures.SpectralSkewness)) title("Spectral Skewness") subtitle("Signal "+signalID) axis tight % Plot the time-frequency ridges nexttile plot(features(infofeatures.TFRidges)) title("Time-Frequency Ridges") subtitle("Signal "+signalID) axis tight signalID = signalID +1; end

### Feature Vectors and Scalars in Time-Frequency Domain

Specify scalarization methods to extract the scalar impulse factor and peak value of the instantaneous energy feature for an oscillating signal.

Set the impulse factor and the peak value as scalarization methods for the instantaneous energy time-frequency domain feature.

opts = scalarFeatureOptions("timefrequency", ... InstantaneousEnergy={'ImpulseFactor';'PeakValue'})

opts = timeFrequencyScalarFeatureOptions with properties: SpectralKurtosis: [0x0 string] SpectralSkewness: [0x0 string] SpectralCrest: [0x0 string] SpectralFlatness: [0x0 string] SpectralEntropy: [0x0 string] TFRidges: [0x0 string] InstantaneousBandwidth: [0x0 string] InstantaneousFrequency: [0x0 string] InstantaneousEnergy: [2x1 string] MeanEnvelopeEnergy: [0x0 string] TimeSpectrum: [0x0 string] WaveletEntropy: [0x0 string] ScaleSpectrum: [0x0 string] All: [0x0 string]

Create a `signalTimeFrequencyFeatureExtractor`

object that returns scalar values for the instantaneous energy feature from the variational mode decomposition of a signal.

tfFE = signalTimeFrequencyFeatureExtractor(Transform="vmd", ... InstantaneousEnergy=true,ScalarizationMethod=opts);

Extract the vector and scalar features for a voltage-controlled oscillating signal.

fs = 10000; t = 0:1/fs:2; x = vco(sawtooth(2*pi*t,0.75),[0.1 0.4]*fs,fs); [features,info] = extract(tfFE,x);

Display the scalar feature values.

```
% Impulse Factor of the Instantaneous Energy Vector
features(info.InstantaneousEnergyImpulseFactor)
```

ans = 8.7551

```
% Peak Value of the Instantaneous Energy Vector
features(info.InstantaneousEnergyPeakValue)
```

ans = 1.3385

### Time-Frequency Ridges Feature Extraction from Signal Spectrogram

Extract the time-frequency ridges from a spectrogram using a `signalTimeFrequencyFeatureExtractor`

object.

Load a data file containing an echolocation pulse `batsignal`

, emitted by a big brown bat (*Eptesicus fuscus*) and measured with a sample rate `DT`

of 7 microseconds. For more information, see the example Find and Track Ridges Using Reassigned Spectrogram.

`load batsignal`

Create a MATLAB® timetable using the signal and the time information.

t = (0:length(batsignal)-1)*DT; sg = timetable(seconds(t)',batsignal);

Create an object to extract time-frequency ridges from the spectrogram of a signal.

fs = 1/DT; sTFFE = signalTimeFrequencyFeatureExtractor( ... Transform="spectrogram",SampleRate=fs,TFRidges=true);

Set the leakage, the time resolution, and the overlap percent parameters for the spectrogram analysis method.

lk = 0.9; tRes = 0.00028; % seconds oPercent = 85; setExtractorParameters(sTFFE,"spectrogram", ... Leakage=lk,TimeResolution=tRes,OverlapPercent=oPercent);

Set the number of ridges, number of frequency bins, and penalty parameters for the time-frequency ridges feature.

nRidges = 3; setExtractorParameters(sTFFE,"TFRidges", ... NumRidges=nRidges,NumFrequencyBins=128,Penalty=0.01);

Extract and plot the time-frequency ridges.

tfRidges = reshape(extract(sTFFE,sg),[],nRidges); tStamps = seconds(tRes/2+(1-oPercent/100)*tRes*(0:length(tfRidges)-1)); plot(tStamps,tfRidges/1000) xlabel("Time") ylabel("Frequency (kHz)")

### Extract Wavelet-Related Time-Frequency Features From Multichannel Signal

Extract the instantaneous frequency of a signal using the wavelet synchrosqueezed transform (WSST), the time-averaged wavelet spectrum using the continuous wavelet transform (CWT), and the wavelet entropy using the maximal overlap discrete wavelet transform (MODWT).

Load an ECG signal corresponding to record 200 of the MIT-BIH Arrhythmia Database [1]. The workspace variable `ecgsig`

contains the signal, and the variable `tm`

contains the sample times. The sample rate is approximately 400 Hz.

```
load mit200
Fs = 400;
```

The signal has 10,000 samples. Reshape the signal into a 1000-by-10 matrix. Each column represents one channel in a multichannel signal. Create a `signalDatastore`

object from the matrix.

ecgsig = reshape(ecgsig,[],10); ecgsig = num2cell(ecgsig,1); sds = signalDatastore(ecgsig,SampleRate=Fs);

Set the mean and standard deviation as scalarization methods for the wavelet entropy feature.

opts = scalarFeatureOptions("timefrequency", ... WaveletEntropy={'Mean','StandardDeviation'});

Create a `signalTimeFrequencyFeatureExtractor`

object that returns:

Wavelet entropy and the scalar values specified in

`opts`

Instantaneous frequency from a WSST

Time-averaged spectrum from a CWT

You can extract instantaneous frequency from time-frequency signal representations created using methods such as the short-time Fourier transform (`"spectrogram"`

), empirical mode decomposition (`"emd"`

), and the maximal overlap discrete wavelet packet transform (`"waveletpacket"`

). Set the time-frequency analysis method to `"synchrosqueezedscalogram"`

. The CWT is the only analysis method you can use to extract the time-averaged wavelet spectrum. The `signalTimeFrequencyFeatureExtractor`

object uses the MODWT, the default analysis method of the `wentropy`

function, to extract the wavelet entropy.

tfFE = signalTimeFrequencyFeatureExtractor( ... SampleRate=Fs, ... Transform="synchrosqueezedscalogram", ... InstantaneousFrequency=true, ... WaveletEntropy=true, ... TimeSpectrum=true, ... ScalarizationMethod=opts);

Preallocate arrays to store the extracted features, including the wavelet entropy, of all the signals. To obtain the dimensions, extract the features from the first signal.

data = read(sds); [~,infofeatures] = extract(tfFE,data); numInstFrq = numel(infofeatures.InstantaneousFrequency); numTimeSpect = numel(infofeatures.TimeSpectrum); numWaveEnt = numel(infofeatures.WaveletEntropy); instFrq = zeros(10,numInstFrq); timeSpect = zeros(10,numTimeSpect); waveEnt = zeros(numWaveEnt,1); waveEntMean = zeros(10,1); waveEntStd = zeros(10,1);

Reset the datastore. Extract the features from all the signals.

reset(sds) ctr = 0; while hasdata(sds) ctr = ctr+1; data = read(sds); [features,infofeatures] = extract(tfFE,data); instFrq(ctr,:) = ... features(infofeatures.InstantaneousFrequency); timeSpect(ctr,:) = ... features(infofeatures.TimeSpectrum); waveEnt(:,ctr) = ... features(infofeatures.WaveletEntropy); waveEntMean(ctr,:) = ... features(infofeatures.WaveletEntropyMean); waveEntStd(ctr,:) = ... features(infofeatures.WaveletEntropyStandardDeviation); end

For each signal, compute the mean and standard deviation directly from the extracted wavelet entropy. Confirm they are equal to the extracted scalar values.

[mean(waveEnt,1)' waveEntMean]

`ans = `*10×2*
0.7675 0.7675
0.7941 0.7941
0.7533 0.7533
0.7465 0.7465
0.8055 0.8055
0.8141 0.8141
0.8048 0.8048
0.7833 0.7833
0.7999 0.7999
0.7910 0.7910

[std(waveEnt,0,1)' waveEntStd]

`ans = `*10×2*
0.1714 0.1714
0.1258 0.1258
0.2063 0.2063
0.1945 0.1945
0.1367 0.1367
0.1123 0.1123
0.1235 0.1235
0.1228 0.1228
0.1123 0.1123
0.1168 0.1168

Display the time-averaged wavelet spectrum of the signals as a waterfall plot.

waterfall(timeSpect) title("Time-Averaged Wavelet Spectrum") xlabel("Frequency Index") ylabel("Channel Index") zlabel("Power")

Display the instantaneous frequency of the signals as a waterfall plot.

waterfall(instFrq) view(30,40) title("Instantaneous Frequency") xlabel("Sample") ylabel("Channel Index") zlabel("Frequency")

## More About

### Scalarization Methods for Signal Features in Time-Frequency Domain

For a given feature vector *v* with *N* elements, the
scalarization method options convert *v* to a scalar *s*
as follows.

`'Mean'`

— Mean, defined as the average value of*v*.$$s=\overline{v}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{v}_{i}}$$

`'StandardDeviation'`

— Standard deviation of the elements of*v*, normalized by*N*-1.$$s=\sqrt{\frac{1}{N-1}{\displaystyle \sum _{i=1}^{N}|{v}_{i}-\overline{v}{|}^{2}}}$$

`'PeakValue'`

— Peak value, defined as the maximum absolute value of*v*.$$s={v}_{p}=\underset{i}{\mathrm{max}}\left|{v}_{i}\right|$$

`'ClearanceFactor'`

— Clearance factor, defined as the ratio between the peak value of*v*and the squared mean of the square roots of the absolute values of*v*.$$s=\frac{{v}_{p}}{{\left(\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\sqrt{\left|{v}_{i}\right|}}\right)}^{2}}$$

`'CrestFactor'`

— Crest factor, defined as the ratio between the peak value of*v*and the root-mean-square value of*v*.$$s=\frac{{v}_{p}}{\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{v}_{i}{}^{2}}}}$$

`'Energy'`

— Energy, defined as the sum of the squared values of*v*.$$s={\displaystyle \sum _{i=1}^{N}{v}_{i}{}^{2}}$$

`'Entropy'`

— Entropy, defined as the sum of*p*log_{2}*p*values, where*p*is the vector of normalized squared values of*v*with respect to their sum.$$s={\displaystyle \sum _{i=1}^{N}{p}_{i}{\mathrm{log}}_{2}{p}_{i}},$$

where

$$p=\frac{{v}^{2}}{{\displaystyle \sum _{i=1}^{N}{v}_{i}{}^{2}}}.$$

**Note**The scalarization method

`'Entropy'`

is not supported for the`WaveletEntropy`

nor the`SpectralEntropy`

features.`'ImpulseFactor'`

— Impulse factor, defined as the ratio between the peak value of*v*and the average absolute value of*v*.$$s=\frac{{v}_{p}}{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\left|{v}_{i}\right|}}$$

`'Kurtosis'`

— Kurtosis, defined as the ratio between the fourth moment of*v*and the squared second moment of*v*.$$s=\frac{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{({v}_{i}-\overline{v})}^{4}}}{{\left[\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{({v}_{i}-\overline{v})}^{2}}\right]}^{2}}$$

`'Skewness'`

— Skewness, defined as the ratio between the third moment of*v*and the second moment of*v*raised to the power of 1.5.$$s=\frac{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{({v}_{i}-\overline{v})}^{3}}}{{\left[\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{({v}_{i}-\overline{v})}^{2}}\right]}^{3/2}}$$

## References

[1] Moody, G.B., and R.G. Mark. “The
Impact of the MIT-BIH Arrhythmia Database.” *IEEE Engineering in Medicine and
Biology Magazine* 20, no. 3 (June 2001): 45–50.
https://doi.org/10.1109/51.932724.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

You cannot generate code directly from

`signalTimeFrequencyFeatureExtractor`

. You can generate C/C++ code from the function returned by`generateMATLABFunction`

.

## Version History

**Introduced in R2024a**

## See Also

### Functions

### Objects

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