# Cross Spectrum (Complex » Single-shot) (G Dataflow)

Version:

Computes the cross power spectrum of two signals.

## 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 x or signal y.

• Waveform
• Waveform in complex double-precision, floating-point numbers
• 1D array of double-precision, floating-point numbers
• 1D 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 x or signal y.

Default: False

## signal x

First input signal.

This input accepts the following data types:

• Waveform
• Waveform 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

## signal y

Second input signal.

This input accepts the following data types:

• Waveform
• Waveform 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

## 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 x or signal y.

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

## 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 x or signal y.

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

Default: 1

## cross spectrum

Cross power spectrum of the input signals.

### f0

Start frequency, in Hz, of the spectrum.

### df

Frequency resolution, in Hz, of the spectrum.

### spectrum

Cross power spectrum of the signals.

## 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 Calculating the Cross Power Spectrum

The cross power, ${S}_{xy}\left(f\right)$, of the signals x(t) and y(t) is defined as

${S}_{xy}\left(f\right)=X*\left(f\right)Y\left(f\right)$

where

• X*(f) is the complex conjugate of X(f)
• X(f)=F{x(t)}
• Y(f)=F{y(t)}

This node uses the FFT or DFT routine to compute the cross power spectrum, which is given by

${S}_{xy}=\frac{1}{{n}^{2}}F*\left\{X\right\}F\left\{Y\right\}$

where Sxy represents the complex sequence cross spectrum and n is the number of samples that can accommodate input sequences signal x and signal y.

The largest cross power that this node can compute by the FFT is 223 (8,388,608 or 8M).

Note

Some textbooks define the cross power spectrum as ${S\prime }_{xy}\left(f\right)=X\left(f\right)Y*\left(f\right)$. If you prefer this definition of cross power to the one specified in this node, take the complex conjugate of the output sequence cross spectrum, because this node operates on the real and imaginary portions separately.

## How the Number of Samples Affects this Node

When the number of samples in the inputs signal x and signal y are equal and are a valid power of 2, such that $n=m={2}^{k}$ for k = 1, 2, 3,..., 23, this node makes direct calls to the FFT routine to compute the complex cross power sequence. This technique is efficient in both execution time and memory management because this node performs the operations in place.

When the number of samples in the inputs signal x and signal y are not equal, this node first resizes the smaller sequence by padding it with zeros to match the size of the larger sequence. If this size is a valid power of 2, such that $\mathrm{max}\left(n,m\right)={2}^{k}$ for k = 1, 2, 3,..., 23, this node computes the cross power spectrum using the FFT. Otherwise, this node uses the slower DFT to compute the cross power spectrum. Thus, the size of the complex output sequence is defined by $\text{size}=\mathrm{max}\left(n,m\right)$.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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