Doppler function

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Description

This function generates Doppler function values for n equally spaced points in [0,1].

Usage

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dopp(norx=1024)

Arguments

norx

the number of data or x values in [0, 1]

Details

Doppler function is introduced by Donoho and Johnstone (1994) and is useful test function evaluating a wavelet shrinkage method.

Value

Doppler function values f(i/n), i=1,…,n and its variability ||f|| = ∑_{i=1}^n (f_i - mena(f))^2 / (n-1) where mena(f) = ∑_{i=1}^n f_i / n.

References

Donoho, D.L. and Johnstone, I.M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425–455.

See Also

heav, ppoly, fg1.

Examples

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testdopp <- dopp(1024)
plot(testdopp$x, testdopp$meanf, xlab="", ylab="", 
     main="Plot of Doppler function", type="l")