# STFT Spectrogram (G Dataflow)

Version:

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.

### 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

## x

Input time-domain signal.

## 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.

### 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

## 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
Hanning 1
Hamming 2
Blackman-Harris 3
Exact Blackman 4
Blackman 5
Flat Top 6
4 Term B-Harris 7
7 Term B-Harris 8
Low Sidelobe 9
Blackman Nuttall 11
Triangle 30
Bartlett-Hanning 31
Bohman 32
Parzen 33
Welch 34
Kaiser 60
Dolph-Chebyshev 61
Gaussian 62
Force 64
Exponential 65

Default: Hanning

### length

Length of the window in samples. If this input is less than or equal to zero, this node sets the input to 64.

Default: 64

## 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

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

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: No error

## 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.

## 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:

• 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:

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

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

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

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