# STFT Spectrogram (G Dataflow)

Last Modified: June 25, 2019

Computes the signal energy distribution in the joint time-frequency domain by using the short-time Fourier transform (STFT) algorithm.  ## time-frequency configuration

Configuration of the FFT size of the STFT. This input determines the number of columns in the output STFT spectrogram.

This input is available only if you wire a waveform or a 1D array of double-precision, floating-point numbers to x. ### force freq bins to power of 2?

A Boolean that determines whether to coerce the frequency bins to a power of 2. If this input is True and the frequency bins is not a power of 2, this node sets the frequency bins to the nearest power of 2.

 True Coerces the frequency bins to a power of 2. False Does not coerce the frequency bins to a power of 2.

Default: True ### exclude Nyquist frequency?

A Boolean that determines whether to exclude the energy at the Nyquist frequency from the output STFT.

 True If the FFT size of the STFT is even and this input is True, the output STFT does not include the energy at the Nyquist frequency. False Includes the energy at the Nyquist frequency.

If the FFT size of the STFT is odd, this node ignores this input.

Default: True ## reset

A Boolean that specifies whether to reset the internal state of the node.

 True Resets the internal state of the node. False Does not reset the internal state of the node.

This input is available only if you wire a double-precision, floating-point number to x.

Default: False ## x

Input time-domain signal.

This input accepts the following data types:

• Waveform
• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers ## time-frequency sampling information

The density to use to sample the signal in the joint time-frequency domain and to define the size of the resulting 2D time-frequency array.

This input changes to time steps if you wire a double-precision, floating-point number to x. ### time steps

Number of samples to shift the sliding window. When this input is less than or equal to zero, this node adjusts this input automatically so that no more than 512 rows exist in output STFT.

Performance Considerations

If you specify a small value for time steps, the node might return a large spectrogram, which requires a long computation time and more memory. NI recommends you set time steps so that the number of rows in STFT spectrogram does not exceed 512. If you need a small sampling rate to observe more details and the signal length is large, divide the signal into smaller segments and compute the spectrogram for each segment.

Default: -1 ### frequency bins

FFT size of the STFT. If this input is less than or equal to zero, this node sets the input to 512. If this input is 1, this node coerces the input to 2.

Default: 512 ## time steps

Number of samples to shift the sliding window. time steps must be greater than 0.

This input changes to time-frequency sampling information if you wire a waveform or a 1D array of double-precision, floating-point numbers to x.

Performance Considerations

Increasing time steps decreases the computation time and reduces memory requirements but also reduces time-domain resolution. Decreasing time steps improves time-domain resolution but increases the computation time and memory requirements.

Default: 1 ## window information

Information about the window to use to compute the STFT. ### type

Type of window to use to compute the STFT.

Name Value Description
Rectangle 0 Applies a rectangle window.
Hanning 1 Applies a Hanning window.
Hamming 2 Applies a Hamming window.
Blackman-Harris 3 Applies a Blackman-Harris window.
Exact Blackman 4 Applies an Exact Blackman window.
Blackman 5 Applies a Blackman window.
Flat Top 6 Applies a Flat Top window.
4 Term B-Harris 7 Applies a 4 Term B-Harris window.
7 Term B-Harris 8 Applies a 7 Term B-Harris window.
Low Sidelobe 9 Applies a Low Sidelobe window.
Blackman Nuttall 11 Applies a Blackman Nutall window.
Triangle 30 Applies a Triangle window.
Bartlett-Hanning 31 Applies a Bartlett-Hanning window.
Bohman 32 Applies a Bohman window.
Parzen 33 Applies a Parzen window.
Welch 34 Applies a Welch window.
Kaiser 60 Applies a Kaiser window.
Dolph-Chebyshev 61 Applies a Dolph-Chebyshev window.
Gaussian 62 Applies a Gaussian window.
Force 64 Applies a Force window.
Exponential 65 Applies an Exponential window.

Default: Hanning ### length

Length of the window in samples. When you wire a waveform or a 1D array of double-precision, floating-point numbers to x, this node sets the input to 64 if length is less than or equal to zero. When you wire a double-precision, floating-point number to x, length must be greater than 0 and less than or equal to the sample length.

Default: 64 ## sample length

Length of each set of data. The node performs computation for each set of data.

sample length must be greater than zero.

This input is available only if you wire a double-precision, floating-point number to x.

Default: 100 ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## window parameter

A value that affects the output coefficients when window type is Kaiser, Gaussian, or Dolph-Chebyshev.

If window type is any other type of window, this node ignores this input.

This input represents the following information for each type of window:

• Kaiser—Beta parameter
• Gaussian—Standard deviation
• Dolph-Chebyshev—The ratio, s, of the main lobe to the side lobe

This input is available only if you wire a waveform or a 1D array of double-precision, floating-point numbers to x.

Default: NaN—Causes this node to set beta to 0 for a Kaiser window, the standard deviation to 0.2 for a Gaussian window, and s to 60 for a Dolph-Chebyshev window ## energy conservation?

A Boolean that determines whether to scale the STFT spectrogram so that the energy in the joint time-frequency domain equals the energy in the time domain.

 True Scales the STFT spectrogram so that the energy in the joint time-frequency domain equals the energy in the time domain. False Does not scale the STFT spectrogram so that the energy in the joint time-frequency domain equals the energy in the time domain.

Default: True ## STFT spectrogram

A 2D array that describes the time waveform energy distribution in the joint time-frequency domain. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Computing the STFT Spectrogram

To compute the output STFT Spectrogram, this node completes the following process.

1. Computes the STFT of the input signal x by using a sliding window to divide the signal into several blocks of data.
2. Applies an N-points fast Fourier transform (FFT) to each block of data to obtain the frequency contents of each block of data, where N is the input frequency bins.
3. The STFT aligns the center of the first sliding window with the first sample of x and extends the beginning of the signal by adding zeros.
4. The sliding window moves time steps samples to the next block of data. If the window moves out of x, this node pads x with zeros.

The following figure shows the procedure this node uses to compute the STFT. ## Algorithm for Calculating the STFT Spectrograms

If the input force freq bins to power of 2? is True and the input frequency bins is not a power of 2, then the following equation holds true:

$K={2}^{\left[{\mathrm{log}}_{2}\left(\text{frequency bins}\right)\right]}$

where is the nearest operation.

Otherwise, K is equal to frequency bins.

If the result of the STFT is the matrix $\text{STFT}\left\{X\right\}$, then the size of $\text{STFT}\left\{X\right\}$ is M-by-K, where the following are true:

• $M=\left\{\begin{array}{cc}⌊\frac{L}{\text{time steps}}⌋+1& \mathrm{if}\text{\hspace{0.17em}}L\text{\hspace{0.17em}}\mathrm{is}\text{\hspace{0.17em}}\mathrm{even}\\ ⌊\frac{L-1}{\text{time steps}}⌋+1& \mathrm{if}\text{\hspace{0.17em}}L\text{\hspace{0.17em}}\mathrm{is}\text{\hspace{0.17em}}\mathrm{odd}\end{array}$
• L is the number of elements in x
• is the round down operation

You can use the $\text{STFT}\left\{X\right\}$ to approximate the energy in the joint time-frequency domain using the following expression:

$\text{time steps}*\sum _{i-0}^{M-1}\sum _{j-0}^{K-1}\text{STFT}{\left\{X\right\}}_{ij}$

This result almost equals the energy in the time domain, as shown in the following expression:

$\sum _{i-0}^{L-1}{|X\left(i\right)|}^{2}$

After computing the STFT of X, this node computes the STFT spectrogram of X. This node calculates the STFT spectrogram as the magnitude square of the elements in $\text{STFT}\left\{X\right\}$. Because the FFT returns symmetric results, this node calculates the STFT spectrogram only on the left half of $\text{STFT}\left\{X\right\}$, as shown in the following equation:

where the following are true:

• $i=0,1,\dots ,M-1$
• $j=0,1,\dots ,N-1$
• $N=\left\{\begin{array}{cc}⌈\frac{K-1}{2}⌉+1& K\text{is odd}\\ ⌈\frac{K-1}{2}⌉+1& K\text{is even and exclude Nyquist frequency? is False}\\ ⌈\frac{K-1}{2}⌉& K\text{is even and exclude Nyquist frequency? is True}\end{array}$
• is the round up operation

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application