SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17

Function summary

• cascade(hk, J = 7)
• daub(p)
• morlet(M, w = 5.0, s = 1.0, complete = True)
• qmf(hk)
• wavedec(amn, hk)

Functions

• cascade(hk, J = 7)

  (x,phi,psi) at dyadic points K/2**J from filter coefficients.
  
  Inputs:
    hk  -- coefficients of low-pass filter
    J   -- values will be computed at grid points $K/2^J$
  
  Outputs:
    x   -- the dyadic points $K/2^J$ for $K=0...N*(2^J)-1$
            where len(hk)=len(gk)=N+1
    phi -- the scaling function phi(x) at x
             $\phi(x) = \sum_{k=0}^{N} h_k \phi(2x-k)$
    psi -- the wavelet function psi(x) at x
             $\psi(x) = \sum_{k=0}^N g_k \phi(2x-k)$
           Only returned if gk is not None
  
  Algorithm:
  
    Uses the vector cascade algorithm described by Strang and Nguyen in
    "Wavelets and Filter Banks"
  
    Builds a dictionary of values and slices for quick reuse.
    Then inserts vectors into final vector at then end
  
  

• daub(p)

  The coefficients for the FIR low-pass filter producing Daubechies wavelets.

  p>=1 gives the order of the zero at f=1/2. There are 2p filter coefficients.

• morlet(M, w = 5.0, s = 1.0, complete = True)

  Complex Morlet wavelet.

  Parameters:	M : int Length of the wavelet. w : float Omega0 s : float Scaling factor, windowed from -s*2*pi to +s*2*pi. complete : bool Whether to use the complete or the standard version.

  Notes:

  The standard version:

  pi**-0.25 * exp(1j*w*x) * exp(-0.5*(x**2))

  This commonly used wavelet is often referred to simply as the Morlet wavelet. Note that, this simplified version can cause admissibility problems at low values of w.

  The complete version:

  pi**-0.25 * (exp(1j*w*x) - exp(-0.5*(w**2))) * exp(-0.5*(x**2))

  The complete version of the Morlet wavelet, with a correction term to improve admissibility. For w greater than 5, the correction term is negligible.

  Note that the energy of the return wavelet is not normalised according to s.

  The fundamental frequency of this wavelet in Hz is given by f = 2*s*w*r / M where r is the sampling rate.

• qmf(hk)

  Return high-pass qmf filter from low-pass

• wavedec(amn, hk)

Imported Names