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DJ.EX

Produce Donoho and Johnstone test functions

DESCRIPTION

Function to produce the blocks, bumps, Doppler and heavisine functions described by Donoho and Johnstone (1994).

USAGE

DJ.EX(n=1024, signal=7, rsnr=7, noisy=F, plotfn=F)

REQUIRED ARGUMENTS

None.

OPTIONAL ARGUMENTS

n: Number of samples of the function required.
signal: A factor that multiples the function values.
rsnr: If Gaussian noise is to be added to the functions then this argument specifies the root signal to noise ratio.
noisy: If T then Gaussian noise is added to the signal so that the root signal to noise ratio is rsnr. If F then just the signals are returned.
plotfn: If T then a plot is produced. If F no plot is produced.

VALUE

A list with four components: blocks, bumps, heavi and doppler containing the sampled signal values for the four types of Donoho and Johnstone test functions. Each of these are deemed to be sampled on an equally spaced grid from 0 to 1.

SIDE EFFECTS

If plotfn is true then a plot of the four test functions is produced.

DETAILS

The Donoho and Johnstone test functions were designed to reproduce various features to be found in real world signals such as jump discontinuities (blocks), spikes (the NMR-like bumps), varying frequency behaviour (Doppler) and jumps/spikes in smooth signals (heavisine).

These functions are most often used for testing wavelet shrinkage methods and comparing them to other nonparametric regression techniques.

Another popular function for this purpose is the Piecewise Polynomial created in Nason and Silverman (1994)

NOTE: This function might not give exactly the same function values as the equivalent function in WaveLab

RELEASE

EXAMPLES

#
# Show a picture of the four test functions with the default args
#
DJ.EX(plotfn=T)

#
# Show a picture of the noisy test functions with the default args
#
DJ.EX(plotfn=T)