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

Function summary

• cc_diff(x, a, b, period = None, _cache = _cache)
• cs_diff(x, a, b, period = None, _cache = _cache)
• diff(x, order = 1, period = None, _cache = _cache)
• hilbert(x, _cache = _cache)
• ihilbert(x)
• itilbert(x, h, period = None, _cache = _cache)
• sc_diff(x, a, b, period = None, _cache = _cache)
• shift(x, a, period = None, _cache = _cache)
• ss_diff(x, a, b, period = None, _cache = _cache)
• tilbert(x, h, period = None, _cache = _cache)

Functions

• cc_diff(x, a, b, period = None, _cache = _cache)

  cc_diff(x, a, b, period=2*pi) -> y

  Return (a,b)-cosh/cosh pseudo-derivative of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = cosh(j*a*2*pi/period)/cosh(j*b*2*pi/period) * x_j

  Input:

  a,b

  Defines the parameters of the sinh/sinh pseudo-differential operator.

  Optional input:

  period

  The period of the sequence x. Default is 2*pi.

  Notes:

  cc_diff(cc_diff(x,a,b),b,a) == x

• cs_diff(x, a, b, period = None, _cache = _cache)

  cs_diff(x, a, b, period=2*pi) -> y

  Return (a,b)-cosh/sinh pseudo-derivative of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = -sqrt(-1)*cosh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j y_0 = 0

  Input:

  a,b

  Defines the parameters of the cosh/sinh pseudo-differential operator.

  period

  The period of the sequence. Default period is 2*pi.

  Notes:

  For even len(x), the Nyquist mode of x is taken zero.

• diff(x, order = 1, period = None, _cache = _cache)

  diff(x, order=1, period=2*pi) -> y
  
  Return k-th derivative (or integral) of a periodic sequence x.
  
  If x_j and y_j are Fourier coefficients of periodic functions x
  and y, respectively, then
  
    y_j = pow(sqrt(-1)*j*2*pi/period, order) * x_j
    y_0 = 0 if order is not 0.
  
  Optional input:
    order
      The order of differentiation. Default order is 1. If order is
      negative, then integration is carried out under the assumption
      that x_0==0.
    period
      The assumed period of the sequence. Default is 2*pi.
  
  Notes:
    If sum(x,axis=0)=0 then
        diff(diff(x,k),-k)==x (within numerical accuracy)
    For odd order and even len(x), the Nyquist mode is taken zero.
  

• hilbert(x, _cache = _cache)

  hilbert(x) -> y
  
  Return Hilbert transform of a periodic sequence x.
  
  If x_j and y_j are Fourier coefficients of periodic functions x
  and y, respectively, then
  
    y_j = sqrt(-1)*sign(j) * x_j
    y_0 = 0
  
  Notes:
    If sum(x,axis=0)==0 then
      hilbert(ihilbert(x)) == x
    For even len(x), the Nyquist mode of x is taken zero.
  

• ihilbert(x)

  ihilbert(x) -> y

  Return inverse Hilbert transform of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = -sqrt(-1)*sign(j) * x_j y_0 = 0

• itilbert(x, h, period = None, _cache = _cache)

  itilbert(x, h, period=2*pi) -> y

  Return inverse h-Tilbert transform of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = -sqrt(-1)*tanh(j*h*2*pi/period) * x_j y_0 = 0

  Optional input: see tilbert.__doc__

• sc_diff(x, a, b, period = None, _cache = _cache)

  sc_diff(x, a, b, period=2*pi) -> y

  Return (a,b)-sinh/cosh pseudo-derivative of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = sqrt(-1)*sinh(j*a*2*pi/period)/cosh(j*b*2*pi/period) * x_j y_0 = 0

  Input:

  a,b

  Defines the parameters of the sinh/cosh pseudo-differential operator.

  period

  The period of the sequence x. Default is 2*pi.

  Notes:

  sc_diff(cs_diff(x,a,b),b,a) == x For even len(x), the Nyquist mode of x is taken zero.

• shift(x, a, period = None, _cache = _cache)

  shift(x, a, period=2*pi) -> y

  Shift periodic sequence x by a: y(u) = x(u+a).

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f

  Optional input:

  period

  The period of the sequences x and y. Default period is 2*pi.

• ss_diff(x, a, b, period = None, _cache = _cache)

  ss_diff(x, a, b, period=2*pi) -> y

  Return (a,b)-sinh/sinh pseudo-derivative of a periodic sequence x.

  If x_j and y_j are Fourier coefficients of periodic functions x and y, respectively, then

  y_j = sinh(j*a*2*pi/period)/sinh(j*b*2*pi/period) * x_j y_0 = a/b * x_0

  Input:

  a,b

  Defines the parameters of the sinh/sinh pseudo-differential operator.

  period

  The period of the sequence x. Default is 2*pi.

  Notes:

  ss_diff(ss_diff(x,a,b),b,a) == x

• tilbert(x, h, period = None, _cache = _cache)

  tilbert(x, h, period=2*pi) -> y
  
  Return h-Tilbert transform of a periodic sequence x.
  
  If x_j and y_j are Fourier coefficients of periodic functions x
  and y, respectively, then
  
    y_j = sqrt(-1)*coth(j*h*2*pi/period) * x_j
    y_0 = 0
  
  Input:
    h
      Defines the parameter of the Tilbert transform.
    period
      The assumed period of the sequence. Default period is 2*pi.
  
  Notes:
    If sum(x,axis=0)==0 and n=len(x) is odd then
      tilbert(itilbert(x)) == x
    If 2*pi*h/period is approximately 10 or larger then numerically
      tilbert == hilbert
    (theoretically oo-Tilbert == Hilbert).
    For even len(x), the Nyquist mode of x is taken zero.
  

Imported Names