In numerical analysis

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

, continuous wavelet

Wavelet

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...

s are functions used by the continuous wavelet transform

Continuous wavelet transform

A continuous wavelet transform is used to divide a continuous-time function into wavelets. Unlike Fourier transform, the continuous wavelet transform possesses the ability to construct a time-frequency representation of a signal that offers very good time and frequency localization...

. These functions are defined as analytical expression

Analytical expression

In mathematics, an analytical expression is a mathematical expression, constructed using well-known operations that lend themselves readily to calculation...

s, as functions either of time or of frequency.
Most of the continuous wavelets are used for both wavelet decomposition and composition transforms. That is they are the continuous counterpart of orthogonal wavelet

Orthogonal wavelet

An orthogonal wavelet is a wavelet where the associated wavelet transform is orthogonal.That is the inverse wavelet transform is the adjoint of the wavelet transform.If this condition is weakened you may end up with biorthogonal wavelets.- Basics :...

s.

The following continuous wavelets have been invented for various applications:

• Morlet wavelet
• Modified Morlet wavelet
  Modified Morlet wavelet
  Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic and hyperbolic tangent pulses...
  
  
• Mexican hat wavelet
• Complex mexican hat wavelet
  Complex mexican hat wavelet
  The complex Mexican hat wavelet is a low-oscillation, complex-valued, wavelet for the continuous wavelet transform. This wavelet is formulated in terms of its Fourier transformas the Hilbert analytic function of the conventional Mexican hat wavelet:...
  
  
• Shannon wavelet
  Shannon wavelet
  - Shannon wavelet or sinc wavelet :Two kinds of Shannon wavelets can be implemented:*Real Shannon wavelet*Complex Shannon waveletThe signal analysis by ideal bandpass filters define a decomposition known as Shannon wavelets...
  
  
• Difference of Gaussians
  Difference of Gaussians
  In computer vision, Difference of Gaussians is a grayscale image enhancement algorithm that involves the subtraction of one blurred version of an original grayscale image from another, less blurred version of the original. The blurred images are obtained by convolving the original grayscale image...
  
  
• Hermitian wavelet
• Hermitian hat wavelet
  Hermitian hat wavelet
  The Hermitian hat wavelet is a low-oscillation, complex-valued wavelet.The real and imaginary parts of this wavelet are defined to be thesecond and first derivatives of a Gaussian respectively:...
  
  
• Beta wavelet
  Beta wavelet
  Continuous wavelets of compact support can be built [1], which are related to the beta distribution. The process is derived from probability distributions using blur derivative. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of...
  
  
• Causal Wavelet
• μ wavelets
• Cauchy wavelet
• Addison wavelet