# pchip: Piecewise cubic hermite interpolation In signal: Signal Processing

## Description

Piecewise cubic hermite interpolation.

## Usage

 `1` ```pchip(x, y, xi = NULL) ```

## Arguments

 `x,y` vectors giving the coordinates of the points to be interpolated. `x` must be strictly monotonic (either increasing or decreasing). `xi` points at which to interpolate.

## Details

In contrast to `spline`, `pchip` preserves the monotonicity of `x` and `y`.

## Value

Normally, the interpolated signal, an array of `length(xi)`.

if `xi == NULL`, a list of class `pp`, a piecewise polynomial representation with the following elements:

 `x` breaks between intervals. `P` a matrix with `n` times `d` rows and `k` columns. The ith row of `P`, `P[i,]`, contains the coefficients for the polynomial over the ith interval, ordered from highest to lowest. There must be one row for each interval in `x`. `n` number of intervals (`length(x) - 1`). `k` polynomial order. `d` number of polynomials.

## Author(s)

Original Octave version by Paul Kienzle pkienzle@user.sf.net. Conversion to R by Tom Short.

## References

Fritsch, F. N. and Carlson, R. E., “Monotone Piecewise Cubic Interpolation”, SIAM Journal on Numerical Analysis, vol. 17, pp. 238-246, 1980.

Octave Forge https://octave.sourceforge.io/

`approx`, `spline`, `interp1`

## Examples

 ```1 2 3 4 5 6 7``` ```xf <- seq(0, 11, length=500) yf <- sin(2*pi*xf/5) xp <- c(0:10) yp <- sin(2*pi*xp/5) pch <- pchip(xp, yp, xf) plot(xp, yp, xlim = c(0, 11)) lines(xf, pch, col = "orange") ```

### Example output ```Attaching package: 'signal'

The following objects are masked from 'package:stats':

filter, poly
```

signal documentation built on May 25, 2021, 9:06 a.m.