Wavelet Transforms, Wavelet Denoising and Wavelet Smoothing in Origin
 
  Skip Navigation Links
 

Wavelet Tools

Wavelet analysis is an accurate and reliable tool for studying signals with sudden changes of phase and frequency. It is useful for audio/image/video analyzing and processing, data compression, signal smoothing and denoising, speech recognition and biomedical imaging. OriginPro's wavelet transform tools support continuous and discrete transforms using standard wavelet families. Tools for multi-scale wavelet decomposition, wavelet smoothing and denoising are also available.

Continuous Wavelet Transform in OriginPro...

The Continuous Wavelet Transform (CWT) tool in OriginPro is capable of computing wavelet coefficients for 1D real or complex signals. Three types of wavelet are supported in this function including Morlet, Mexican Hat and the derivative of Gaussian wavelets.

Continuouse Wavelet Transform Tool
magnifying_glassView larger image


View Example

Single-Level 1D Discrete Wavelet Transform in OriginPro...

OriginPro supplies a Wavelet Decomposition (DWT) tool for one-dimensional, single-level discrete wavelet decomposition. It also provides a Wavelet Reconstruction (IDWT) tool for reconstructing a signal from its coefficients that are generated by DWT. Both tools support standard wavelet families such as Haar, Daubechies and Biorthogonal wavelets. When performing wavelet decomposition or reconstruction, you can specify how to pad the signals to get enough samples to compute the output corresponding to the data points near the boundaries. Two methods for padding are available: zero-padding and periodic padding (this method treats the input signal as a periodic signal and pads the sequence with repeated pattern).

Wavelet Decomposition and Reconstruction Example
View Example


DWT Dialog IDWT Dialog

magnifying_glassView larger image

magnifying_glassView larger image

Single-Level 2D Discrete Wavelet Transform in OriginPro...

OriginPro also supports 2D wavelet decomposition and reconstruction. The 2D Wavelet Decomposition (DWT2) tool is capable of decomposing a 2D signal that is saved in a matrix into its approximation coefficients, horizontal detail coefficients, vertical detail coefficients and diagonal detail coefficients. On the other hand, the 2D Wavelet Reconstruction (IDWT2) tool can reconstruct the 2D signal from these coefficients. The 2D Wavelet Deconstruction and Reconstruction tools support standard wavelet families such as Haar, Daubechies and Biorthogonal wavelets.

DWT2_Dialog IDWT2 Dialog

magnifying_glassView larger image

magnifying_glassView larger image


2D Wavelet Transform Example
View Example

Multi-Level 1D Discrete Wavelet Transform in OriginPro...

The Multi-Level Wavelet Transform (MDWT) tool in OriginPro performs multi-level 1D discrete wavelet decomposition. You can specify the level for the decomposition and choose a wavelet type from Haar, Daubechies and Biorthogonal wavelets to perform the decomposition.

MDWT Dialog

Wavelet Denoising in OriginPro...

The Wavelet Denoising (WTDENOISE) tool in OriginPro removes noise from signals using wavelet transform. Compared to denoising based on Fourier Transforms, Wavelet Denoising works better in preserving the shape of the real signal, especially for signals with abrupt changes. The computation of Wavelet Denoising is actually based on multi-level 1D discrete wavelet transform. After decomposing the input signal into many levels, this tool uses thresholding to change the values of the detail coefficients. Then it performs inverted wavelet transform on the approximation coefficients and the altered detail coefficients. The result is a denoised signal. The level for the wavelet decomposition, the wavelet type and the method to perform the thresholding can be customized in the dialog of this tool.

Wavelet Smoothing Example
View Example

Wavelet Denoising Tool

Wavelet Smoothing in OriginPro...

The Wavelet Smoothing (WTSMOOTH) tool in OriginPro performs smoothing to signals using wavelet transform. This kind of smoothing works quite well in preserving the shape of the real signal, even for signals with abrupt changes. Similar to wavelet denoising, the computation of wavelet smoothing is based on multi-level 1D discrete wavelet transform. The detail coefficients are altered after the decomposition, and then used to reconstruct the real signal with the approximation coefficients. The difference is that in Wavelet Smoothing, some detail coefficients are set to zero if their indexes are greater than a certain number, while in Wavelet Denoising, whether a detail coefficient will be altered depends on its value. In the Wavelet Smoothing tool, you can customize the multi-level decomposition by specifying the level for decomposition and the wavelet type. Further, you can specify the percentage of detail coefficients to be cut off.


View Example

Wavelet Smoothing Tool

Note: OriginPro includes the ability to automatically recalculate the analysis results of the above operations any time you change the parameters or update your source data. In addition, the settings for any of these analysis routines can be saved to an analysis theme for use later with similar data.

Skip Navigation Links.
Copyright © 2012 OriginLab Corporation. All rights reserved.
20+ years serving the scientific and engineering community