Multiresolution Approximation

DESCRIPTION:

Performs a multiresolution approximation of a signal.

USAGE:

mra(x, ...) 

REQUIRED ARGUMENTS:

x
a time series object or a dwt object. When x is an object of class "dwt", all the additional arguments will be ignored.

OPTIONAL ARGUMENTS:

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

VALUE:

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

DETAILS:

Multiresolution analysis can be used to provide a series of coarse to fine approximations 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. Generic functions crystal.names, print, plot have methods for mra objects.

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 <- mra(x1, wavelet="s8") 
m2 <- mra(x2, wavelet="s8") 
plot(m1) 
plot(m2)