Preprocessing

A few functions (i.e. wavelet transforms) are provided for data preprocessing purposes.

Discrete Wavelet Transform

Discrete Wavelet Transform based on the GSL DWT [Gsldwt].

mlpy.dwt(x, wf, k)

Discrete Wavelet Tranform

Input

• x - [1D numpy array float] data
• wf - [string] wavelet type (‘d’: daubechies, ‘h’: haar, ‘b’: bspline)
• k - [integer] member of the wavelet family
  • daubechies: k = 4, 6, ..., 20 with k even
  • haar: the only valid choice of k is k = 2
  • bspline: k = 103, 105, 202, 204, 206, 208, 301, 303, 305 307, 309

Output

• X - [1D numpy array float] discrete wavelet transform

mlpy.idwt(X, wf, k)

Inverse Discrete Wavelet Tranform

Input

• X - [1D numpy array float] data
• wf - [string] wavelet type (‘d’: daubechies, ‘h’: haar, ‘b’: bspline)
• k - [integer] member of the wavelet family
  • daubechies: k = 4, 6, ..., 20 with k even
  • haar: the only valid choice of k is k = 2
  • bspline: k = 103, 105, 202, 204, 206, 208, 301, 303, 305 307, 309

Output

• x - [1D numpy array float]

Continuous Wavelet Transform

Continuous Wavelet Transform based on [Torrence98].

mlpy.cwt(x, dt, dj, wf='dog', p=2, pad=0.0)

Continuous Wavelet Tranform.

Input

• x - [1D numpy array float] data
• dt - [float] time step
• dj - [float] scale resolution (smaller values of dt give finer resolution)
• wf - [string] wavelet function (‘morlet’, ‘paul’, ‘dog’)
• p - [float] wavelet function parameter
• pad - [float] minimum fraction of added zeros (zero padding)

Output

• X, scales - (scales x angularfreq) [2D numpy array complex], scales [1D numpy array float]

mlpy.icwt(X, dt, dj, wf='dog', p=2, recf=True)

Inverse Continuous Wavelet Tranform.

Input

• X - (scales x angularfreq) [2D numpy array complex]

• dt - [float] time step

• dj - [float] scale resolution (smaller values of dt give finer resolution)

• wf - [string] wavelet function (‘morlet’, ‘paul’, ‘dog’)

• p - [int] wavelet function parameter

  • morlet: 2, 4, 6
  • paul: 2, 4, 6
  • dog: 2, 6, 10

• recf - [bool] use the reconstruction factor (Cdelta*psi_0(0))

Output

• x - [1D numpy array float]

Other functions

See [Torrence98].

mlpy.angularfreq(N, dt)

Compute angular frequencies.

Input

• N - [integer] number of data samples
• dt - [float] time step

Output

• angular frequencies - [1D numpy array float]

mlpy.scales(N, dj, dt, s0)

Compute scales.

Input

• N - [integer] number of data samples
• dj - [float] scale resolution
• dt - [float] time step

Output

• scales - [1D numpy array float]

mlpy.compute_s0(dt, p, wf)

Compute s0.

Input

• dt - [float] time step
• p - [float] omega0 (‘morlet’) or order (‘paul’, ‘dog’)
• wf - [string] wavelet function (‘morlet’, ‘paul’, ‘dog’)

Output

• s0 - [float]

[Torrence98]

(1, 2) C Torrence and G P Compo. Practical Guide to Wavelet Analysis

[Gsldwt]

Gnu Scientific Library, http://www.gnu.org/software/gsl/