stftLayer
Description
An STFT layer computes the short-time Fourier transform of the input. Use of this layer requires Deep Learning Toolbox™.
Creation
Description
creates a Short-Time Fourier Transform (STFT) layer. The input to
layer
= stftLayerstftLayer
must be a real-valued dlarray
(Deep Learning Toolbox) object in
"CBT"
format with a size along the time dimension greater than the
length of Window
. stftLayer
formats the output as
"SCBT"
.
For more information, see Layer Output Format.
sets properties using one or more name-value arguments. You can specify the analysis
window and the number of overlapped samples, among others.layer
= stftLayer(Name=Value
)
Properties
STFT
Window
— Analysis window
hann
(128,'periodic')
(default) | vector
hann
(128,'periodic')This property is read-only.
Analysis window used to compute the STFT, specified as a vector with two or more elements.
Example: (1-cos(2*pi*(0:127)'/127))/2
and
both specify a Hann window of
length 128.hann
(128)
Data Types: double
| single
OverlapLength
— Number of overlapped samples
96
(default) | positive integer
This property is read-only.
Number of overlapped samples, specified as a positive integer strictly smaller
than the length of Window
.
The stride between consecutive windows is the difference between the window length and the number of overlapped samples.
Data Types: double
| single
FFTLength
— Number of DFT points
128
(default) | positive integer
This property is read-only.
Number of frequency points used to compute the discrete Fourier transform, specified as a positive integer greater than or equal to the window length. If not specified, this argument defaults to the length of the window.
Data Types: double
| single
TransformMode
— Layer transform mode
"mag"
(default) | "squaremag"
| "logmag"
| "logsquaremag"
| "realimag"
Layer transform mode, specified as one of these:
"mag"
— STFT magnitude"squaremag"
— STFT squared magnitude"logmag"
— Natural logarithm of the STFT magnitude"logsquaremag"
— Natural logarithm of the STFT squared magnitude"realimag"
— Real and imaginary parts of the STFT, concatenated along the channel dimension
Data Types: char
| string
Layer
WeightLearnRateFactor
— Multiplier for weight learning rate
0
(default) | nonnegative scalar
Multiplier for weight learning rate, specified as a nonnegative scalar. If not
specified, this property defaults to zero, resulting in weights that do not update
with training. You can also set this property using the setLearnRateFactor
(Deep Learning Toolbox) function.
Data Types: double
| single
Name
— Layer name
""
(default) | character vector | string scalar
Layer name, specified as a character vector or string scalar.
For Layer
array input, the trainnet
(Deep Learning Toolbox) and
dlnetwork
(Deep Learning Toolbox) functions automatically assign
names to layers with the name ""
.
The stftLayer
object stores this property as a character vector.
Data Types: char
| string
NumInputs
— Number of inputs
1
(default)
This property is read-only.
Number of inputs to the layer, returned as 1
. This layer accepts a
single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is read-only.
Input names, returned as {'in'}
. This layer accepts a single input
only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is read-only.
Number of outputs from the layer, returned as 1
. This layer has a
single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is read-only.
Output names, returned as {'out'}
. This layer has a single output
only.
Data Types: cell
Examples
Short-Time Fourier Transform of Chirp
Generate a signal sampled at 600 Hz for 2 seconds. The signal consists of a chirp with sinusoidally varying frequency content. Store the signal in a deep learning array with "CTB"
format.
fs = 6e2;
x = vco(sin(2*pi*(0:1/fs:2)),[0.1 0.4]*fs,fs);
dlx = dlarray(x,"CTB");
Create a short-time Fourier transform layer with default properties. Create a dlnetwork
object consisting of a sequence input layer and the short-time Fourier transform layer. Specify a minimum sequence length of 128 samples. Run the signal through the predict
method of the network.
ftl = stftLayer; dlnet = dlnetwork([sequenceInputLayer(1,MinLength=128) ftl]); netout = predict(dlnet,dlx);
Convert the network output to a numeric array. Use the squeeze
function to remove the length-1 channel and batch dimensions. Plot the magnitude of the STFT. The first dimension of the array corresponds to frequency and the second to time.
q = extractdata(netout); waterfall(squeeze(q)') set(gca,XDir="reverse",View=[30 45]) xlabel("Frequency") ylabel("Time")
Short-Time Fourier Transform of Sinusoid
Generate a 3 × 160 (× 1) array containing one batch of a three-channel, 160-sample sinusoidal signal. The normalized sinusoid frequencies are π/4 rad/sample, π/2 rad/sample, and 3π/4 rad/sample. Save the signal as a dlarray
, specifying the dimensions in order. dlarray
permutes the array dimensions to the "CBT"
shape expected by a deep learning network.
nch = 3;
N = 160;
x = dlarray(cos(pi.*(1:nch)'/4*(0:N-1)),"CTB");
Create a short-time Fourier transform layer that can be used with the sinusoid. Specify a 64-sample rectangular window, 48 samples of overlap between adjoining windows, and 1024 DFT points. By default, the layer outputs the magnitude of the STFT.
stfl = stftLayer(Window=rectwin(64), ... OverlapLength=48, ... FFTLength=1024);
Create a two-layer dlnetwork
object containing a sequence input layer and the STFT layer you just created. Treat each channel of the sinusoid as a feature. Specify the signal length as the minimum sequence length for the input layer.
layers = [sequenceInputLayer(nch,MinLength=N) stfl]; dlnet = dlnetwork(layers);
Run the sinusoid through the forward
method of the network.
dataout = forward(dlnet,x);
Convert the network output to a numeric array. Use the squeeze
function to collapse the size-1 batch dimension. Permute the channel and time dimensions so that each array page contains a two-dimensional spectrogram. Plot the STFT magnitude separately for each channel in a waterfall plot.
q = squeeze(extractdata(dataout)); q = permute(q,[1 3 2]); for kj = 1:nch subplot(nch,1,kj) waterfall(q(:,:,kj)') view(30,45) zlabel("Ch. "+string(kj)) end
More About
Short-Time Fourier Transform
The short-time Fourier transform (STFT) is used to analyze how the frequency content of a nonstationary signal changes over time. The magnitude squared of the STFT is known as the spectrogram time-frequency representation of the signal. For more information about the spectrogram and how to compute it using Signal Processing Toolbox™ functions, see Spectrogram Computation with Signal Processing Toolbox.
The STFT of a signal is computed by sliding an analysis window g(n) of length M over the signal and calculating the discrete Fourier transform (DFT) of each segment of windowed data. The window hops over the original signal at intervals of R samples, equivalent to L = M – R samples of overlap between adjoining segments. Most window functions taper off at the edges to avoid spectral ringing. The DFT of each windowed segment is added to a complex-valued matrix that contains the magnitude and phase for each point in time and frequency. The STFT matrix has
columns, where Nx is the length of the signal x(n) and the ⌊⌋ symbols denote the floor function. The number of rows in the matrix equals NDFT, the number of DFT points, for centered and two-sided transforms and an odd number close to NDFT/2 for one-sided transforms of real-valued signals.
The mth column of the STFT matrix contains the DFT of the windowed data centered about time mR:
Layer Output Format
stftLayer
formats the output as "SCBT"
, a sequence
of 1-D images where the image height corresponds to frequency, the second dimension
corresponds to channel, the third dimension corresponds to batch, and the fourth dimension
corresponds to time.
You can feed the output of
stftLayer
unchanged to a 1-D convolutional layer when you want to convolve along the frequency ("S"
) dimension. For more information, seeconvolution1dLayer
(Deep Learning Toolbox).To feed the output of
stftLayer
to a 1-D convolutional layer when you want to convolve along the time ("T"
) dimension, you must place a flatten layer after thestftLayer
. For more information, seeflattenLayer
(Deep Learning Toolbox).You can feed the output of
stftLayer
unchanged to a 2-D convolutional layer when you want to convolve along the frequency ("S"
) and time ("T"
) dimensions. For more information, seeconvolution2dLayer
(Deep Learning Toolbox).To use
stftLayer
as part of a recurrent neural network, you must place a flatten layer after thestftLayer
. For more information, seelstmLayer
(Deep Learning Toolbox) andgruLayer
(Deep Learning Toolbox).To use the output of
stftLayer
with a fully connected layer as part of a classification workflow, you must reduce the time ("T"
) dimension of the output so that it has size 1. To reduce the time dimension of the output, place a global pooling layer before the fully connected layer. For more information, seeglobalAveragePooling2dLayer
(Deep Learning Toolbox) andfullyConnectedLayer
(Deep Learning Toolbox).
Version History
Introduced in R2021bR2023b: Weights initialized to analysis window
Starting in R2023b, stftLayer
initializes the
Weights
learnable parameter to the analysis window used to compute
the transform. Previously, the parameter was initialized to an array containing the Gabor
atoms for the STFT.
R2022b: OutputMode
property to be removed in a future release
The OutputMode
property of stftLayer
will be
removed in a future release. Update your code and networks to make them compatible with
stftLayer
output in "SCBT"
format. For more
information, see Layer Output Format.
See Also
Apps
- Deep Network Designer (Deep Learning Toolbox)
Objects
istftLayer
|dlarray
(Deep Learning Toolbox) |dlnetwork
(Deep Learning Toolbox)
Functions
dlstft
|stft
|dlistft
|istft
|stftmag2sig
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
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