# Wavelet Transform Daubechies4 (G Dataflow)

Version:

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

## x

The input sequence.

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

## error in

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

Default: No error

## wavelet daubechies4{x}

The wavelet Daubechies4 transform of the input sequence.

## error out

Error information. The node produces this output according to standard error behavior.

## Algorithm Definition

The Wavelet Transform Daubechies4 transform can be defined using the following transformation matrix:

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

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

$\mathrm{Wavelet}\text{\hspace{0.17em}}\mathrm{Daubechies}4\left\{X\right\}=C*X$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported