# Deconvolution (G Dataflow)

Computes the deconvolution of two sequences.

The deconvolution operation is performed using Fourier transform pairs.

## 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 when either of the input sequences is a double-precision, floating-point number.

Default: False

## x * y

The set of input data.

This input accepts the following data types:

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

The number of elements in x * y must be greater than or equal to the number of elements in y. If the number of elements in x * y is less than the number of elements in y, the node sets x to an empty array and returns an error.

## y

The set of dependent values.

This input accepts the following data types:

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

## sample length x * y

Length of each set of input data. This node computes each set of data separately.

This node returns an empty array if sample length y is greater than sample length x * y.

This input is available only if x * y is a double-precision, floating-point number.

Default: 100

## sample length y

Length of each set of dependent values. This node computes each set of values separately.

sample length y must be greater than 0. This node returns an empty array if sample length y is greater than sample length x * y.

This input is available only if y is a double-precision, floating-point number.

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

## x

The deconvolved sequence.

This output can return the following data types:

• 1D array of double-precision, floating-point numbers
• Waveform
• 1D array of waveforms

The number of elements in x is n - m + 1 where n is the number of elements in x * y and m is the number of elements in y.

## 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 Deconvolution of a Signal

This node can use Fourier identities to derive the deconvolution operation because $x\left(t\right)*y\left(t\right)⇔X\left(f\right)Y\left(f\right)$ is a Fourier transform pair, where the symbol * denotes convolution, and the deconvolution is the inverse of the convolution operation. If h(t) is the signal resulting from the deconvolution of the signals x(t) and y(t), the Deconvolution node obtains h(t) using the following equation:

$h\left(t\right)={F}^{-1}\left(\frac{X\left(f\right)}{Y\left(f\right)}\right)$

where X(f) is the Fourier transform of x(t), and Y(f) is the Fourier transform of y(t).

## Performing the Discrete Implementation of the Deconvolution

This node performs the discrete implementation of the deconvolution using the following steps.

1. Compute the Fourier transform of the input sequence x * y.
2. Compute the Fourier transform of the input sequence y.
3. Divide the Fourier transform of x * y by the Fourier transform of y. Call the new sequence h.
4. Compute the inverse Fourier transform of h to obtain the deconvolved sequence x.
Note

When there are zeros in the Fourier transform of the input sequence y, the deconvolution operation may fail.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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