Fast Chebyshev Transform (1D)

Transfroms between nodal and spectral values.

Description

This script allows for fast transformation between nodal and spectral values at the Chebyshev-Gauss-Lobatto points by using the built-in functions fft/ifft. I've tested it with truncation as high as N=2^20 and it takes 1.7820 seconds. This script will handle an arbitrary number of data sets of the same length simultaneously.

• Acknowledgements: This submission has inspired the following:; ORTHPOLYFIT, ORTHPOLYVAL
• MATLAB release: MATLAB 7 (R14)

[ZHANG Zhongqiang]

In fact, the codes are incorrect.I found it in one perform. And I give another one .

[Greg von Winckel]

Thanks. I forgot to upload the fix earlier. Line 20 should be

B=([F(1,:); 2*F(2:(N-1),:); F(N,:)]);

[sid tal]

why doesn't this work for derivatives, when I use the standard iterative scheme to get the modes of the differentiated function?

[duncan sutherland]

There appears to be a bug in the spectral to nodal transform for the highest mode, transforming (0,0,0,0,1) for example gives T_4/2 rather than T_4.

[Farbod]

can we extend this script to 3D?

[rajesh]

how to write matlab code for discrete chebyshev transform ?