If we want to perform some other type of interpolation, we need to specify the fourth argument. The MATLAB function “interp1()” computes interpolated values using the default settings that correspond to linear interpolation. In our case, this vector is called “time_dense”. The third argument is a set of values on the x axis at which we want to compute the interpolated values. In our case, the first two arguments are “time_coarse” and “coarse_function” which are used to define the original function values.
The first two arguments are the set of points that define the original function. The MATLAB function “interp1()” is used to interpolate the function values. Plot(time_coarse,coarse_function,'o',time_dense,dense_function_interpolated,'.') % Vq = interp1(X,V,Xq) interpolates to find Vq, the values of the underlying function V=F(X) at the query points Xq.ĭense_function_interpolated = interp1(time_coarse,coarse_function,time_dense) The array is reshaped internally to a matrix where the leadingĪnd each row of this matrix is then treated separately.Coarse_function=time_coarse.^2-0.1*time_coarse.^3 If y is an array, then the size of y must have the form Values of the vector y are the values of the first derivative of the If the length of y is n + 2, then the first and last Y is n, then the "not-a-knot" end condition is used. The variable x must be a vector of length n. When called with a third input argument, spline evaluates the spline That may be used with ppval to evaluate the polynomial at specific When called with two arguments, return the piecewise polynomial pp Return the cubic spline interpolant of points x and y. : pp = spline ( x, y) ¶ : yi = spline ( x, y, xi) ¶ Underlie the interp1 function can be called directly. In addition, the support functions spline and lookup that An example of the use of interpft isįigure 29.3: Comparison of interp1 and interpft for non-periodic data Signal and its interpolation are required to be sampled at equispaced Signals will be poorly represented at the edges. The function signal is assumed to be periodic, and so non-periodic There are two significant limitations on Fourier interpolation. Interpft assumes that the interpolated function is periodic, and soĪssumptions are made about the endpoints of the interpolation. If dim is specified, then interpolate along the dimension dim. N-dimensional array, the interpolation is performed on each column of Theĭata in x is assumed to be equispaced. If x is a vector then x is resampled with n points. : y = interpft ( x, n) ¶ : y = interpft ( x, n, dim) ¶ 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 Next: Multi-dimensional Interpolation, Up: Interpolation
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