interpft

1-D interpolation (FFT method)

Syntax

y = interpft(X,n)

y = interpft(X,n,dim)

Description

y = interpft(X,n) interpolates the Fourier transform of the function values in X to produce n equally spaced points. interpft operates on the first dimension whose size does not equal 1.

y = interpft(X,n,dim) operates along dimension dim. For example, if X is a matrix, then interpft(X,n,2) operates on the rows of X.

Examples

Fourier Interpolation

Interpolate 1-D data using the FFT method and visualize the result.

Generate some sample points in the interval $$[0,3\pi ]$$ for the function $$f(x)={\sin }^2(x)\cos (x)$$. Use a spacing interval dx to ensure the data is evenly spaced. Plot the sample points.

dx = 3*pi/30;
x = 0:dx:3*pi;
f = sin(x).^2 .* cos(x);
plot(x,f,'o')

Use FFT interpolation to find the function value at 200 query points.

N = 200;
y = interpft(f,N);

Calculate the spacing of the interpolated data from the spacing of the sample points with dy = dx*length(x)/N, where N is the number of interpolation points. Truncate the data in y to match the sampling density of x2.

dy = dx*length(x)/N;
x2 = 0:dy:3*pi;
y = y(1:length(x2));

Plot the results.

hold on
plot(x2,y,'.')
title('FFT Interpolation of Periodic Function')

Interpolate Rows of Data

Generate three separate data sets of normally distributed random numbers. Assume the data is sampled at the positive integers, 1:N. Store the data sets as rows in a matrix.

A = randn(3,20);
x = 1:20;

Interpolate the rows of the matrix at 500 query points each. Specify dim = 2 so that interpft works on the rows of A.

N = 500;
y = interpft(A,N,2);

Calculate the spacing interval of the interpolated data dy. Truncate the data in y to match the sampling density of x2.

dy = length(x)/N;
x2 = 1:dy:20;
y = y(:,1:length(x2));

Plot the results.

subplot(3,1,1)
plot(x,A(1,:)','o');
hold on
plot(x2,y(1,:)','--')
title('Row 1')

subplot(3,1,2)
plot(x,A(2,:)','o');
hold on
plot(x2,y(2,:)','--')
title('Row 2')

subplot(3,1,3)
plot(x,A(3,:)','o');
hold on
plot(x2,y(3,:)','--')
title('Row 3')

Input Arguments

X — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, matrix, or multidimensional array. The data in X is assumed to be sampled at an evenly spaced interval of the independent variable. interpft works best with periodic data.

Data Types: single | double
Complex Number Support: Yes

n — Number of points

positive integer scalar

Number of points, specified as a positive integer scalar.

Data Types: single | double

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

• interpft(X,n,1) interpolates the columns of X.

  

• interpft(X,n,2) interpolates the rows of X.

  

Example: interpft(X,n,3)

Output Arguments

y — Interpolated points

vector | matrix | multidimensional array

Interpolated points, returned as a vector, matrix, or multidimensional array. If length(X,dim) = m, and X has a sampling interval of dx, then the new sampling interval for y is dy = dx*m/n, where n > m.

If dim is specified, then interpft pads or truncates X to length n in dimension dim, so that size(y,dim) = n.

Algorithms

The interpft function uses the FFT method. The original vector x is transformed to the Fourier domain using fft, and then it is transformed back with more points.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The input argument n must be a fixed-size scalar at code generation time.

• For input argument X:

  • If you do not specify a dimension, the code generator operates along the first dimension of the input array that is variable size or whose size does not equal 1. If this dimension is variable size at code generation time and is 1 at run time, a run-time error can occur. To avoid this error, specify the dimension.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a