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dcht

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Returns the Chebyshev interpolation coefficients. The amplitude of the coefficients decreases exponentially and the last coefficient offers an estimate of the relative accuracy of the interpolation.

 

Supported Product: FDTD, MODE

 

Syntax

Description

coeff=dcht(f,option);

Returns the Chebyshev interpolation coefficients of a sampled function f. The function f must be sampled on a Chebyshev roots grid.

 

Option:

If option=1 is selected, the vector x will not include the endpoints

If option=2 is selected, the vector x will include the endpoints

 

Example

This example shows how to obtain interpolation coefficients from a sampled function:

Nc = 15;         # Number of sample points

xmin = 0;

xmax = 1;

x = chpts(xmin,xmax,Nc,1); # Returns Chebyshev roots grid on interval between xmin and xmax

f = exp(1i*2*pi*x);    # Function sampling using Chebyshev grid

coeff = dcht(f,1);     # Get interpolation coefficients

?abs(coeff);

result: 

0.304242  

0.569231  

0.970868  

0.666917  

0.302849  

0.104282  

0.0290919  

0.00684063  

0.00139224  

0.000250007  

4.01899e-005  

5.85025e-006  

7.78278e-007  

9.53372e-008  

1.094e-008      

 

See Also

chpts, chebin, icht, chebpol, chebpol1

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