dcmri.stepconv#

dcmri.stepconv(f, T, D, t=None, dt=1.0)[source]#

Convolve a 1D-array with a normalised step function.

Parameters:

  • f (array_like) – the 1D array to be convolved.

  • T (float) – the central time point of the step function.

  • D (float) – half-width of the step function, as a fraction of T. D must be less or equal to 1.

  • t (array_like, optional) – the time points where the values of f are defined, in the same units as T. If t=None, the time points are assumed to be uniformly spaced with spacing dt. Defaults to None.

  • dt (float, optional) – spacing between time points for uniformly spaced time points. This parameter is ignored if t is explicity provided. Defaults to 1.0.

Raises:

ValueError – if D > 1.

Returns:

a 1D numpy array of the same length as f.

Return type:

numpy.ndarray

See also

conv, expconv, biexpconv, nexpconv

Notes

stepconv implements the same convolution product as conv, but is more accurate and faster in the special case where one of the factors is known to be a step function.

Example

Import package, create a vector f and an array of time points:

>>> import dcmri as dc
>>> f = [5,4,3,6]
>>> t = [0,2,4,7]

Convolve f with a step function that is centered on t=3 with a half width of 1.5 = 0.5*3:

>>> dc.stepconv(f, 3, 0.5, t)
array([0.        , 0.8125    , 3.64583333, 3.5625    ])

Examples using dcmri.stepconv#

A comparison of convolution functions

A comparison of convolution functions