MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of
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2 Polynomials and Interpolation<br />
interpolation methods, see the section “Comparing Interpolation Methods” on<br />
page 2-13.<br />
FFT-Based Interpolation<br />
The function interpft performs one-dimensional interpolation using an<br />
FFT-based method. This method calculates the Fourier transform <strong>of</strong> a vector<br />
that contains the values <strong>of</strong> a periodic function. It then calculates the inverse<br />
Fourier transform using more points. Its form is<br />
y = interpft(x,n)<br />
x is a vector containing the values <strong>of</strong> a periodic function, sampled at equally<br />
spaced points. n is the number <strong>of</strong> equally spaced points to return.<br />
Two-Dimensional Interpolation<br />
The function interp2 performs two-dimensional interpolation, an important<br />
operation for image processing and data visualization. Its most general form is<br />
ZI = interp2(X,Y,Z,XI,YI,method)<br />
Z is a rectangular array containing the values <strong>of</strong> a two-dimensional function,<br />
and X and Y are arrays <strong>of</strong> the same size containing the points for which the<br />
values in Z are given. XI and YI are matrices containing the points at which to<br />
interpolate the data. method is an optional string specifying an interpolation<br />
method.<br />
There are three different interpolation methods for two-dimensional data:<br />
• Nearest neighbor interpolation (method = 'nearest'). This method fits a<br />
piecewise constant surface through the data values. The value <strong>of</strong> an<br />
interpolated point is the value <strong>of</strong> the nearest point.<br />
• Bilinear interpolation (method = 'linear'). This method fits a bilinear<br />
surface through existing data points. The value <strong>of</strong> an interpolated point is a<br />
combination <strong>of</strong> the values <strong>of</strong> the four closest points. This method is piecewise<br />
bilinear, and is faster and less memory-intensive than bicubic interpolation.<br />
• Bicubic interpolation (method = 'cubic'). This method fits a bicubic surface<br />
through existing data points. The value <strong>of</strong> an interpolated point is a<br />
combination <strong>of</strong> the values <strong>of</strong> the sixteen closest points. This method is<br />
piecewise bicubic, and produces a much smoother surface than bilinear<br />
interpolation. This can be a key advantage for applications like image<br />
2-12
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