# `signal.bsplines`¶

## Module Contents¶

### Functions¶

 `factorial`(n) `spline_filter`(Iin,lmbda=5.0) Smoothing spline (cubic) filtering of a rank-2 array. `_bspline_piecefunctions`(order) Returns the function defined over the left-side pieces for a bspline of `bspline`(x,n) B-spline basis function of order n. `gauss_spline`(x,n) Gaussian approximation to B-spline basis function of order n. `cubic`(x) A cubic B-spline. `quadratic`(x) A quadratic B-spline. `_coeff_smooth`(lam) `_hc`(k,cs,rho,omega) `_hs`(k,cs,rho,omega) `_cubic_smooth_coeff`(signal,lamb) `_cubic_coeff`(signal) `_quadratic_coeff`(signal) `cspline1d`(signal,lamb=0.0) Compute cubic spline coefficients for rank-1 array. `qspline1d`(signal,lamb=0.0) Compute quadratic spline coefficients for rank-1 array. `cspline1d_eval`(cj,newx,dx=1.0,x0=0) Evaluate a spline at the new set of points. `qspline1d_eval`(cj,newx,dx=1.0,x0=0) Evaluate a quadratic spline at the new set of points.
`factorial`(n)
`spline_filter`(Iin, lmbda=5.0)

Smoothing spline (cubic) filtering of a rank-2 array.

Filter an input data set, Iin, using a (cubic) smoothing spline of fall-off lmbda.

`_bspline_piecefunctions`(order)

Returns the function defined over the left-side pieces for a bspline of a given order.

The 0th piece is the first one less than 0. The last piece is a function identical to 0 (returned as the constant 0). (There are order//2 + 2 total pieces).

Also returns the condition functions that when evaluated return boolean arrays for use with numpy.piecewise.

`bspline`(x, n)

B-spline basis function of order n.

Uses numpy.piecewise and automatic function-generator.

`gauss_spline`(x, n)

Gaussian approximation to B-spline basis function of order n.

`cubic`(x)

A cubic B-spline.

This is a special case of bspline, and equivalent to `bspline(x, 3)`.

`quadratic`(x)

A quadratic B-spline.

This is a special case of bspline, and equivalent to `bspline(x, 2)`.

`_coeff_smooth`(lam)
`_hc`(k, cs, rho, omega)
`_hs`(k, cs, rho, omega)
`_cubic_smooth_coeff`(signal, lamb)
`_cubic_coeff`(signal)
`_quadratic_coeff`(signal)
`cspline1d`(signal, lamb=0.0)

Compute cubic spline coefficients for rank-1 array.

Find the cubic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 .

signal : ndarray
A rank-1 array representing samples of a signal.
lamb : float, optional
Smoothing coefficient, default is 0.0.
c : ndarray
Cubic spline coefficients.
`qspline1d`(signal, lamb=0.0)

Compute quadratic spline coefficients for rank-1 array.

Find the quadratic spline coefficients for a 1-D signal assuming mirror-symmetric boundary conditions. To obtain the signal back from the spline representation mirror-symmetric-convolve these coefficients with a length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 .

signal : ndarray
A rank-1 array representing samples of a signal.
lamb : float, optional
Smoothing coefficient (must be zero for now).
c : ndarray
Cubic spline coefficients.
`cspline1d_eval`(cj, newx, dx=1.0, x0=0)

Evaluate a spline at the new set of points.

dx is the old sample-spacing while x0 was the old origin. In other-words the old-sample points (knot-points) for which the cj represent spline coefficients were at equally-spaced points of:

oldx = x0 + j*dx j=0…N-1, with N=len(cj)

Edges are handled using mirror-symmetric boundary conditions.

`qspline1d_eval`(cj, newx, dx=1.0, x0=0)

Evaluate a quadratic spline at the new set of points.

dx is the old sample-spacing while x0 was the old origin. In other-words the old-sample points (knot-points) for which the cj represent spline coefficients were at equally-spaced points of:

```oldx = x0 + j*dx  j=0...N-1, with N=len(cj)
```

Edges are handled using mirror-symmetric boundary conditions.