Wavelet Transform Daubechies4 (Not in Base Package)

Performs the wavelet transform based on the Daubechies4 function. Details  

	X is the samples of the input signal. The length of the signal has to be a power of 2, otherwise an error code is given.
	Wavelet Daubechies4 {X} returns the calculated wavelet Daubechies4 transform.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Wavelet Transform Daubechies4 Details

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

.

Here blank entries signify zeroes. The numbers c₀, c₁, c₂, and c₃ have to fulfill certain orthogonal properties

c₀² + c₁² + c₂² + c₃² = 1

c₂c₀ + c₃c₁ = 0

c₃ – c₂ + c₁ – c₀ = 0

0c₃ – 1c₂ + 2c₁ – 3c₀ = 0

with the unique solution

.

Note  You can solve the previous system of nonlinear equations in c0, c1, c2, and c3 directly with the Nonlinear System Single Solution VI of this package.

The Wavelet Daubechies4 transform of the array X is defined by

Wavelet Daubechies4{X} = C * X