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**Owning Palette:** Discrete Wavelet VIs

**Requires:** Advanced Signal Processing Toolkit

Computes the multi-level undecimated wavelet transform (UWT) of **signal**. This VI returns the approximation coefficients at the largest level and the detail coefficients at all levels for a 1D signal input and returns the approximation coefficients and the detail coefficients at all levels for a 2D signal input. The approximation coefficients and the detail coefficients at all levels are the same size as **signal**. The results of the UWT have the translation invariant property, which is helpful in robust feature extraction and pattern recognition. Wire data to the **signal** input to determine the polymorphic instance to use or manually select the instance.

Use the pull-down menu to select an instance of this VI.

signal specifies the input signal. | |||||

levels specifies the number of levels in the discrete wavelet analysis. levels must be a positive integer no greater than log2(Ls), where Ls is the length of the 1D signal or the minimum dimensional size of the 2D signal. Otherwise, you can set the value to –1, which indicates that this VI sets levels as the largest integer no greater than log2(Ls). The default is –1. | |||||

wavelet specifies the wavelet type to use for the discrete wavelet analysis. The default is db02. The options include two types: orthogonal (Haar, Daubechies (db), Coiflets (xxcoif), Symmlets (xsym)) and biorthogonal (Biorthogonal (xbior), including FBI (x_xbior4_4 (FBI))), where x indicates the order of the wavelet. The higher the order, the smoother the wavelet. The orthogonal wavelets are not redundant and are suitable for signal or image denoising and compression. The biorthogonal wavelets usually have the linear phase property and are suitable for signal or image feature extraction. If you want to use other types of wavelets, do not wire this input. Instead, use the Wavelet Design Express VI to design the wavelet you want and wire the resulting analysis filters to the analysis filters input.
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error in describes error conditions that occur before this node runs. This input provides standard error in functionality. | |||||

analysis filters specifies the coefficients of the lowpass analysis filters and the highpass analysis filters for the wavelet you specify. If you specify a value for analysis filters, this VI ignores the settings in the wavelet input. You can use the Wavelet Design Express VI to design the analysis filters and the corresponding synthesis filters.
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UWT coef returns the approximation coefficients and the detail coefficients from the multi-level undecimated wavelet transform (UWT) concatenated into an array of waveforms starting with the approximation coefficients at the largest level followed by the detail coefficients at all levels in descending order. You can use the WA Get Coefficients of Undecimated Wavelet Transform VI to read the approximation coefficients or detail coefficients at a specific level. Wire UWT coef to the UWT coef input of the WA Get Coefficients of Undecimated Wavelet Transform VI.
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error out contains error information. This output provides standard error out functionality. |

signal specifies the input signal. | |||||

levels specifies the number of levels in the discrete wavelet analysis. levels must be a positive integer no greater than log2(Ls), where Ls is the length of the 1D signal or the minimum dimensional size of the 2D signal. Otherwise, you can set the value to –1, which indicates that this VI sets levels as the largest integer no greater than log2(Ls). The default is –1. | |||||

wavelet specifies the wavelet type to use for the discrete wavelet analysis. The default is db02. The options include two types: orthogonal (Haar, Daubechies (db), Coiflets (xxcoif), Symmlets (xsym)) and biorthogonal (Biorthogonal (xbior), including FBI (x_xbior4_4 (FBI))), where x indicates the order of the wavelet. The higher the order, the smoother the wavelet. The orthogonal wavelets are not redundant and are suitable for signal or image denoising and compression. The biorthogonal wavelets usually have the linear phase property and are suitable for signal or image feature extraction. If you want to use other types of wavelets, do not wire this input. Instead, use the Wavelet Design Express VI to design the wavelet you want and wire the resulting analysis filters to the analysis filters input.
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error in describes error conditions that occur before this node runs. This input provides standard error in functionality. | |||||

analysis filters specifies the coefficients of the lowpass analysis filters and the highpass analysis filters for the wavelet you specify. If you specify a value for analysis filters, this VI ignores the settings in the wavelet input. You can use the Wavelet Design Express VI to design the analysis filters and the corresponding synthesis filters.
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UWT coef returns the approximation coefficients and the detail coefficients from the multi-level undecimated wavelet transform (UWT). The first row of UWT coef contains the approximation coefficients at the largest level. The other rows contain the detail coefficients at all levels in descending order. You can use the WA Get Coefficients of Undecimated Wavelet Transform VI to read the approximation coefficients or detail coefficients at a specific level. Wire UWT coef to the UWT coef input of the WA Get Coefficients of Undecimated Wavelet Transform VI.
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error out contains error information. This output provides standard error out functionality. |

signal specifies the 2D input signal. | |||||||||

levels specifies the number of levels in the discrete wavelet analysis. levels must be a positive integer no greater than log2(Ls), where Ls is the length of the 1D signal or the minimum dimensional size of the 2D signal. Otherwise, you can set the value to –1, which indicates that this VI sets levels as the largest integer no greater than log2(Ls). The default is –1. | |||||||||

wavelet specifies the wavelet type to use for the discrete wavelet analysis. The default is db02. The options include two types: orthogonal (Haar, Daubechies (db), Coiflets (xxcoif), Symmlets (xsym)) and biorthogonal (Biorthogonal (xbior), including FBI (x_xbior4_4 (FBI))), where x indicates the order of the wavelet. The higher the order, the smoother the wavelet. The orthogonal wavelets are not redundant and are suitable for signal or image denoising and compression. The biorthogonal wavelets usually have the linear phase property and are suitable for signal or image feature extraction. If you want to use other types of wavelets, do not wire this input. Instead, use the Wavelet Design Express VI to design the wavelet you want and wire the resulting analysis filters to the analysis filters input.
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error in describes error conditions that occur before this node runs. This input provides standard error in functionality. | |||||||||

analysis filters specifies the coefficients of the lowpass analysis filters and the highpass analysis filters for the wavelet you specify. If you specify a value for analysis filters, this VI ignores the settings in the wavelet input. You can use the Wavelet Design Express VI to design the analysis filters and the corresponding synthesis filters.
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UWT coef returns the approximation coefficients and the detail coefficients from the multi-level undecimated wavelet transform (UWT). Each element of the array contains the 2D UWT results of one level. The i^{th} element stores the approximation coefficients and the detail coefficients at level i+1. You can use the WA Get Coefficients of Undecimated Wavelet Transform VI to read the approximation coefficients or detail coefficients at a specific level. Wire UWT coef to the UWT coef input of the WA Get Coefficients of Undecimated Wavelet Transform VI.
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error out contains error information. This output provides standard error out functionality. |

The following illustration shows an example of a three-level UWT, where you set the **levels** input of this VI to 3. The length of the input signal is 16 points.

where the subscript indicates the up-sampling by a factor of *m*. Using information in the previous illustration, you can see that the **UWT coef** output contains the approximation coefficients of the largest level and the detail coefficients of each level.

In addition, compared to the discrete wavelet transform (DWT), the UWT does not have sub-sampling. Therefore, the output of each level has the same length as the input signal.

Undecimated discrete wavelet transform is translation-invariant. In other words, when the input signal shifts with certain taps, the output coefficients shift by the same taps, which is important for robust feature extractions, such as peak detection.

Refer to A Wavelet Tour of Signal Processing for more information about the UWT.

Refer to the following VIs for examples of using the WA Undecimated Wavelet Transform VI:

- High-order Discontinuity Detection VI: labview\examples\Wavelet Analysis\WAGettingStarted
- Undecimated Image Decomposition and Reconstruction (UWT) VI: labview\examples\Wavelet Analysis\WAGettingStarted
- Undecimated Signal Decomposition and Reconstruction (UWT) VI: labview\examples\Wavelet Analysis\WAGettingStarted

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