# Wavelet Transform Daubechies4 Inverse (G Dataflow)

Version:

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

## wavelet daubechies4{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

## x

The inverse 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 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:

$\mathrm{Wavelet}\text{\hspace{0.17em}}\mathrm{Daubechies}4\text{\hspace{0.17em}}\mathrm{Inv}\left\{X\right\}={C}^{-1}*X$

where $C{C}^{-1}={C}^{-1}C=I$

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: Not supported