Single-level discrete 1-D wavelet transform
[cA,cD] = dwt(X,
[cA,cD] = dwt(X,Lo_D,Hi_D)
[cA,cD] = dwt(...,'mode',MODE)
dwt command performs
a single-level one-dimensional wavelet decomposition with respect
to either a particular wavelet (
wfilters for more information)
or particular wavelet decomposition filters (
that you specify.
[cA,cD] = dwt(X, computes
the approximation coefficients vector
cA and detail
cD, obtained by a wavelet decomposition
of the vector
X. The string
the wavelet name.
[cA,cD] = dwt(X,Lo_D,Hi_D) computes the
wavelet decomposition as above, given these filters as input:
Lo_D is the decomposition low-pass
Hi_D is the decomposition high-pass
Hi_D must be
the same length.
lx = the length of
the length of the filters
length(cA) = length(cD)
= la where
la = ceil(lx/2), if the DWT
extension mode is set to periodization. For the other extension modes,
For more information about the different Discrete Wavelet Transform
extension modes, see
[cA,cD] = dwt(...,'mode',MODE) computes
the wavelet decomposition with the extension mode
MODE is a string containing the desired
[cA,cD] = dwt(x,'db1','mode','sym');
Obtain the level-1 DWT of the noisy Doppler signal using a wavelet name.
load noisdopp; [A,D] = dwt(noisdopp,'sym4');
Obtain the level-1 DWT of the noisy Doppler signal using wavelet and scaling filters.
load noisdopp; [Lo_D,Hi_D] = wfilters('bior3.5','d'); [A,D] = dwt(noisdopp,Lo_D,Hi_D);
Starting from a signal s of length N, two sets of coefficients are computed: approximation coefficients CA1, and detail coefficients CD1. These vectors are obtained by convolving s with the low-pass filter Lo_D for approximation and with the high-pass filter Hi_D for detail, followed by dyadic decimation.
More precisely, the first step is
The length of each filter is equal to 2L. For signal of length N, the signals F and G are of length N + 2L − 1, and then the coefficients CA1 and CD1 are of length
To deal with signal-end effects involved by a convolution-based
algorithm, a global variable managed by
used. This variable defines the kind of signal extension mode used.
The possible options include zero-padding (used in the previous example)
and symmetric extension, which is the default mode.
For the same input, this
To make the
Daubechies, I. (1992), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics. SIAM Ed.
Mallat, S. (1989), "A theory for multiresolution signal decomposition: the wavelet representation," IEEE Pattern Anal. and Machine Intell., vol. 11, no. 7, pp. 674–693.
Meyer, Y. (1990), Ondelettes et opérateurs, Tome 1, Hermann Ed. (English translation: Wavelets and operators, Cambridge Univ. Press. 1993.)