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Wavelet Analysis

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.

Wavelet analysis expands input signals in terms of translated and dilated version of mother wavelets. The coefficients corresponding to each scale are calculated and can be manipulated individually to emphasize some particular feature.

OriginPro provides the following wavelet analysis tools:


1D Continuous Wavelet Transform

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:

  • Morlet
  • Derivative of Gaussian
  • Mexican Hat

 


1D Discrete Wavelet Transform

OriginPro also supports 2D wavelet decomposition and reconstruction. Both tools support standard wavelet families such as Haar, Daubechies and Biorthogonal wavelets of different orders.

 

  • 1D Wavelet Decomposition
    The 1D Discrete Wavelet Transform (DWT) tool in OriginPro is capable of computing both approximation coefficients and detail coefficients according to the specified wavelet type and its order.

 

  • 1D Wavelet Reconstruction
    The 1D Inverse Discrete Wavelet Transform (IDWT) tool in Origin Pro is capable of reconstructing the 1D signal from the approximation and detail coefficients from a specified wavelet type.

 

  • Multi-Level 1D Wavelet Decomposition
    The 1D Multi-Level Discrete Wavelet Transform (MDWT) tool in OriginPro is capable of computing approximation coefficients and detail coefficients at different decomposition levels for specified wavelet type and its order.

2D Wavelet Transform

OriginPro also supports 2D wavelet decomposition and reconstruction. Both tools support standard wavelet families such as Haar, Daubechies and Biorthogonal wavelets of different orders.

 

  • 2D Wavelet Reconstruction
    The 2D Inverse Discrete Wavelet Transform (IDWT2) tool can reconstruct the 2D signal from approximation coefficients, horizontal, vertical and diagonal detail coefficients from a specified wavelet type.

 

  • 2D Wavelet Decomposition
    The 2D Discrete Wavelet Transform (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 according to a specified wavelet type.

Wavelet Denoising and Smoothing

OriginPro supplies Wavelet Denoising (WTDENOISE) tool to remove noise from signals as well as Wavelet Smoothing (WTSMOOTH) tool to smooth signals using wavelet transform.

 

  • Wavelet Denoising
    The Wavelet Denoising tool removes signal noise based on multi-level 1D discrete wavelet transform. The degrees of denoising can be controlled by adjusting the level for the wavelet decomposition, the wavelet type and the method to perform the thresholding.

 

  • Wavelet Smoothing
    The Wavelet Smoothing (WTSMOOTH) tool smoothes signals based on multi-level 1D discrete wavelet transform. The degrees of smoothing is controlled by the cut-off percentage of detail coefficients..
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