# Wavelet Transform Daubechies4 Inverse (G Dataflow)

Computes the inverse of the wavelet transform based on the Daubechies4 function of a sequence.

## 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 wavelet daubechies4{x}.

Default: False

## wavelet daubechies4{x}

The input sequence.

The length of the sequence must be a power of 2, otherwise this node returns an error.

This input accepts a double-precision, floating-point number or a 1D array of 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 wavelet daubechies4{x}.

Default: 128

## 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 inverse wavelet Daubechies4 transform of the input sequence.

## 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 Definition

The Wavelet Transform Daubechies4 Inverse transform can be defined with the help of the following transformation matrix:

$C=\left[\begin{array}{cccccccccc}{c}_{0}& {c}_{3}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{2}& \text{\hspace{0.17em}}{c}_{1}\\ {c}_{1}& {-c}_{2}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{3}& {-c}_{0}\\ {c}_{2}& {c}_{1}& {c}_{0}& {c}_{3}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ {c}_{3}& {-c}_{0}& {c}_{1}& {-c}_{2}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& .& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& .& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{2}& {c}_{1}& {c}_{0}& {c}_{3}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{1}& {-c}_{0}& {c}_{1}& {-c}_{2}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{2}& {c}_{1}& {c}_{0}& {c}_{3}\\ \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& \text{\hspace{0.17em}}& {c}_{3}& {-c}_{0}& {c}_{1}& {-c}_{2}\end{array}\right]$

The inverse Wavelet Daubechies4 transform of an array X is defined by the following equation:

WaveletDaubechies4Inv{X} = C-1 * X

where CC-1 = C-1C = I

The following diagram shows the Wavelet Transform Daubechies4 Inverse of a function with two spikes at the points 13 and 69. The signal length is 1024.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices