Multiresolution Decomposition

DESCRIPTION:

Performs a multiresolution decomposition of a signal.

USAGE:

mrd(x, ...) 

REQUIRED ARGUMENTS:

x
a vector or a time series.

OPTIONAL ARGUMENTS:

...
additional arguments for dwt. See dwt for details.

VALUE:

an object of class "mrd", inheriting from class "decompose". See decompose.object for details.

DETAILS:

A multiresolution decomposition separates a signal into orthogonal components based on wavelets at different resolution levels (scales). For details, refer to Chapter 5 of Daubechies (1992) and to the section "Multiresolution Analysis" in the S+WAVELETS User's Manual.

REFERENCES:

Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.

Mallat, S. (1989). A Theory of Multiresolution Signal Decomposition: the Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intellingence, 11 (7), 674-693.

SEE ALSO:

, , , .

EXAMPLES:

par(mfrow=c(1, 2)) 
x1 <- make.signal("doppler", n=256)          # noiseless doppler 
x2 <- make.signal("doppler", n=256, snr=7)   # noisy doppler 
m1 <- mrd(x1, wavelet="s8") 
m2 <- mrd(x2, wavelet="s8") 
plot(m1) 
plot(m2)