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The starting condition returned by this function is computed based on the following transfer function:: cs H(z) = ------------------- (1 - a2 z - a3 z^2) where:: a2 = (2 r cos omega) a3 = - r^2 cs = 1 - 2 r cos omega + r^2 Parameters ---------- input : ndarray The input signal. r, omega : float Parameters in the transfer function. precision : float Specifies the precision for calculating initial conditions of the recursive filter based on mirror-symmetric input. Returns ------- zi : ndarray The mirror-symmetric initial condition for the forward IIR filter.out = symiirorder2_ic_fwd(input, r, omega, precision=-1.0) Compute the (forward) mirror-symmetric boundary conditions for a smoothing IIR filter that is composed of cascaded second-order sections. The starting condition returned by this function is computed based on the following transfer function:: cs H(z) = ------------------- (1 - a2/z - a3/z^2) where:: a2 = (2 r cos omega) a3 = - r^2 cs = 1 - 2 r cos omega + r^2 Parameters ---------- input : ndarray The input signal. r, omega : float Parameters in the transfer function. precision : float Specifies the precision for calculating initial conditions of the recursive filter based on mirror-symmetric input. Returns ------- zi : ndarray The mirror-symmetric initial condition for the forward IIR filter.out = symiirorder1_ic(input, z1, precision=-1.0) Compute the (forward) mirror-symmetric boundary conditions for a smoothing IIR filter that is composed of cascaded first-order sections. The starting condition returned by this function is computed based on the following transfer function:: 1 H(z) = ------------ (1 - z1/z) Parameters ---------- input : ndarray The input signal. If 2D, then it will find the initial conditions for each of the elements on the last axis. z1 : scalar Parameter in the transfer function. precision : Specifies the precision for calculating initial conditions of the recursive filter based on mirror-symmetric input. Returns ------- z_0 : ndarray The mirror-symmetric initial condition for the forward IIR filter.out = sepfir2d(input, hrow, hcol) Convolve with a 2-D separable FIR filter. Convolve the rank-2 input array with the separable filter defined by the rank-1 arrays hrow, and hcol. Mirror symmetric boundary conditions are assumed. This function can be used to find an image given its B-spline representation. Parameters ---------- input : ndarray The input signal. Must be a rank-2 array. hrow : ndarray A rank-1 array defining the row direction of the filter. Must be odd-length hcol : ndarray A rank-1 array defining the column direction of the filter. Must be odd-length Returns ------- output : ndarray The filtered signal. 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