FFT Power Spectrum and PSD (Power Spectrum » Single-shot) (G Dataflow) - LabVIEW Communications System Design Suite 4.0 Manual

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Last Modified: June 25, 2019

Computes the single-sided or double-sided power spectrum of a time-domain signal.

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 one of the following data types to signal:

Waveform
Waveform in complex double-precision, floating-point numbers
1D array of waveforms
1D array of waveforms in complex double-precision, floating-point numbers
1D array of double-precision, floating-point numbers
1D array of complex double-precision, floating-point numbers
2D array of double-precision, floating-point numbers
2D array of complex double-precision, floating-point numbers

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

window type

Time-domain window to apply to the signal.

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 Nutall	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: Rectangle

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 signal.

Default: False

signal

The input time-domain signal, usually in volts.

The time-domain record must contain at least three cycles of the signal for a valid estimate.

This input accepts the following data types:

Waveform
Waveform in complex double-precision, floating-point numbers
1D array of waveforms
1D array of waveforms in complex double-precision, floating-point numbers
Double-precision, floating-point number
1D array of double-precision, floating-point numbers
1D array of complex double-precision, floating-point numbers
2D array of double-precision, floating-point numbers
2D array of complex double-precision, floating-point numbers

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 signal.

Default: 100

dB on

A Boolean that specifies whether this node returns the results in decibels.

True	Returns the results in decibels.
False	Returns the results in the original units.

Default: False

single-sided

A Boolean specifying whether this node computes the single-sided or double-sided power spectrum.

True	Computes the single-sided power spectrum.
False	Computes the double-sided power spectrum.

This input is available only if you wire one of the following data types to signal:

Waveform
1D array of waveforms
Double-precision, floating-point number
1D array of double-precision, floating-point numbers
2D array of double-precision, floating-point numbers

Default: False

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

dt

Sample period of the time-domain signal in seconds.

Set this input to 1/fs, where fs is the sampling frequency of the time-domain signal.

This input is available only if you wire one of the following data types to signal:

Double-precision, floating-point number
1D array of double-precision, floating-point numbers
1D array of complex double-precision, floating-point numbers
2D array of double-precision, floating-point numbers
2D array of complex double-precision, floating-point numbers

Default: 1

power spectrum

Power spectrum of the input signal.

This output can return a cluster or a 1D array of clusters.

f0

Start frequency, in Hz, of the spectrum.

df

Frequency resolution, in Hz, of the spectrum.

magnitude

Magnitude of the power spectrum.

Determining the unit of measurement

If the input signal is in volts (V), the unit of this output is volts-rms squared (V_rms² ) for power spectrum. If the input signal is not in volts, the units of this output is the input signal unit-rms squared for power spectrum. If this node returns results in decibels, and the input signal is in volts, the units of this output is dBV for power spectrum.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

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 Power Spectrum

If single-sided is True, this node first computes the double-sided power spectrum, and then converts the power spectrum into a single-sided power spectrum.

This node uses the fast Fourier transform (FFT) and discrete Fourier transform (DFT) routines to compute the double-sided power spectrum, which is given by the following equation:

S_{x x} = \frac{{| F {X} |}^{2}}{n^{2}}

where

x is the input signal
S_xx is the output sequence power spectrum
n is the number of samples in the input signal

When the number of samples in the input signal is a valid power of 2, such that $n = 2^{m}$ for $m = 1, 2, 3, ..., 23$ , this node computes the fast Fourier transform of a real-valued sequence using the fast radix-2 FFT algorithm and efficiently scales the magnitude square. The largest power spectrum the node can compute using the FFT is 2²³ (8,388,608 or 8M).

When the number of samples in the input signal is not a valid power of 2 but is factorable as the product of small prime numbers, this node computes the discrete Fourier transform of a real-valued sequence using an efficient DFT algorithm and scales the magnitude square. The largest power spectrum the node can compute using the fast DFT is 2²² - 1 (4,194,303 or 4M - 1).

Let Y be the Fourier transform of the input signal and n be the number of samples in it. Then the following equation is true.

{| Y_{n - i} |}^{2} = | Y_{- i}^{2} |

You can interpret the power in the (n - i)^th element of Y as the power in the -i^th element of the sequence, which represents the power in the -i^th harmonic. You can find the total power for the i^th harmonic (excluding DC and Nyquist components) by using the following equation.

\begin{matrix} 2 {| Y_{i} |}^{2} = {| Y_{i} |}^{2} + {| Y_{n - 1} |}^{2} & 0 < i < \frac{n}{2} \end{matrix}

The total power in the DC and Nyquist components are ${| Y_{0} |}^{2}$ and ${| Y_{\frac{n}{2}} |}^{2}$ respectively.

If n is even, let $k = \frac{n}{2}$ . The following table shows the format of the output sequence S_xx corresponding to power spectrum.

Array Element of Double-Sided Spectrum	Array Element of Single-Sided Spectrum	Interpretation
S_xx₀	S_xx₀	Power in DC component
S_xx₁ = S_{xx_(n-1)}	S_xx₁ * 2	Power at frequency Δf
S_xx₂ = S_{xx_(n-2)}	S_xx₂ * 2	Power at frequency 2Δf
S_xx₃ = S_{xx_(n-3)}	S_xx₃ * 2	Power at frequency 3Δf
$⋮$	$⋮$	$⋮$
S_{xx_(K-2)} = S_{xx_n-(k-2)}	S_{xx_(k-2)} * 2	Power at frequency (k - 2)Δf
S_{xx_(K-1)} = S_{xx_n-(k-1)}	S_{xx_(K-1)} * 2	Power at frequency (k - 1)Δf
S_{XX_k}	S_{XX_k}	Power in Nyquist harmonic

If n is odd, let $k = \frac{n - 1}{2}$ . The following table shows the format of the output sequence S_xx corresponding to power spectrum.

Array Element of Double-Sided Spectrum	Array Element of Single-Sided Spectrum	Interpretation
S_xx₀	S_xx₀	Power in DC component
S_xx₁ = S_{xx_(n-1)}	S_xx₁ * 2	Power at frequency Δf
S_xx₂ = S_{xx_(n-2)}	S_xx₂ * 2	Power at frequency 2Δf
S_xx₃ = S_{xx_(n-3)}	S_xx₃ * 2	Power at frequency 3Δf
$⋮$	$⋮$	$⋮$
S_{xx_(K-2)} = S_{xx_n-(k-2)}	S_{xx_(K-2)} * 2	Power at frequency (k - 2)Δf
S_{xx_(K-1)} = S_{xx_n-(k-1)}	S_{xx_(K-1)} * 2	Power at frequency (k - 1)Δf
S_{XX_(n-k)}	S_{xx_k} * 2	Power at frequency kΔf

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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

Table Of Contents

FFT Power Spectrum and PSD (Power Spectrum » Single-shot) (G Dataflow)

window parameter

window type

reset

signal

sample length

dB on

single-sided

error in

dt

power spectrum

f0

df

magnitude

error out

Algorithm for Computing the Power Spectrum

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