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