Interpolation methods for a step functionįourier interpolation, is a resampling technique where a signal isĬonverted to the frequency domain, padded with zeros and then "linear" methods in all other cases, the x-values must beįigure 29.2: Comparison of the second derivative of the "pchip" and "spline" Or right-continuous interpolant, respectively.ĭiscontinuous interpolation is only allowed for "nearest" and The options "left" or "right" to select a left-continuous The continuity condition of the interpolant may be specified by using If x is decreasing, the default discontinuous If x is increasing, the default discontinuous interpolant is May be at most 2 consecutive points with the same value. There is an equivalence, such that ppval (interp1 ( x,ĭuplicate points in x specify a discontinuous interpolant. Object can later be used with ppval to evaluate the interpolation. If the string argument "pp" is specified, then xi should notīe supplied and interp1 returns a piecewise polynomial object. Number, then replace values beyond the endpoints with that number. If extrap is the string "extrap", then extrapolate valuesīeyond the endpoints using the current method. This is usually faster,Īnd is never slower.
To assume that x is uniformly spaced, and only x(1)Īnd x(2) are referenced. Interpolation with smooth first derivative.Ĭubic spline interpolation-smooth first and second derivativesĪdding ’*’ to the start of any method above forces interp1 Piecewise cubic Hermite interpolating polynomial-shape-preserving Linear interpolation from nearest neighbors. If y is a matrix or an N-dimensionalĪrray, the interpolation is performed on each column of y. If not specified, x is taken to be the indices of y Interpolate input data to determine the value of yi at the points Polynomial InterpolationĪnd Interpolation on Scattered Data describe additional methods.
Octave supports several methods for one-dimensional interpolation, most A Practical Guide to Splines, Springer-Verlag, 1978.Next: Multi-dimensional Interpolation, Up: Interpolation Interpn Multidimensional data interpolation (table lookup) Interp3 Three-dimensional data interpolation (table lookup) Interp2 Two-dimensional data interpolation (table lookup) See Also interpft One-dimensional interpolation using the FFT method. For access to the more advanced features, see these M-files and the Spline Toolbox. spline uses them in a fairly simple fashion to perform cubic spline interpolation. These routines form a small suite of functions for working with piecewise polynomials. For the ' spline' method, interp1 calls a function spline that uses the M-files ppval, mkpp, and unmkpp. The ' nearest', ' linear' and ' cubic' methods have fairly straightforward implementations. Then the population in 1975, obtained by table lookup within the matrix tab, isĪlgorithm The interp1 command is a MATLAB M-file. If a portion of the census data is stored in a single 5-by-2 table, Sometimes it is more convenient to think of interpolation in table lookup terms where the data are stored in a single table. Now interpolate within the data at every year from 1900 to 2000, and plot the result. The expression interp1(t,p,1975) interpolates within the census data to estimate the population in 1975. P = Described in table lookup terms, the table is tab = and interp1 looks up the elements of xi in x, and, based upon their locations, returns values yi interpolated within the elements of y.Įxamples Here are two vectors representing the census years from 1900 to 1990 and the corresponding United States population in millions of people. Interpolation is the same operation as table lookup.
This is shown below, along with the relationship between vectors x, Y, xi, and yi. It finds values of a one-dimensional function f(x) underlying the data at intermediate points. The interp1 command interpolates between data points. For faster interpolation when x is equally spaced, use the methods '* linear', '* cubic', '* nearest', or '* spline'. 'spline' for cubic spline interpolationĪll the interpolation methods require that x be monotonic.'nearest' for nearest neighbor interpolation.Out of range values are returned as NaNs.
If Y is a matrix, then the interpolation is performed for each column of Y and yi will be length(xi)-by- size(Y,2). The vector x specifies the points at which the data Y is given. Returns vector yi containing elements corresponding to the elements of xi and determined by interpolation within vectors x and Y. One-dimensional data interpolation (table lookup) Interp1 (MATLAB Function Reference) MATLAB Function Reference
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