Owning Palette: Transforms VIs
Requires: Full Development System
Computes the inverse of the wavelet transform based on the Daubechies4 function of the input sequence X.
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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. |
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Wavelet Daubechies4 Inv {X} returns the calculated inverse wavelet Daubechies4 transform. |
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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. |
The Wavelet Transform Daubechies4 Inverse transform can be defined with the help of the transformation matrix
.
Here blank entries signify zeros. The numbers c0, c1, c2, and c3 have to fulfill certain orthogonal properties, namely
c02 + c12 + c22 + c32 = 1
c2c0 + c3c1 = 0
c3 – c2 + c1 – c0 = 0
0c3 – 1c2 + 2c1 – 3c0 = 0
with the unique solution
.
The inverse Wavelet Daubechies4 transform of the array X is defined by
Wavelet Daubechies4 Inv {X} = C–1*X.
It is
CC–1 = C–1C = I.
Refer to the definition of the Wavelet Transform Daubechies4 VI for more information about the Wavelet Transform Daubechies4 transform.
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.
