Number of wavelet coefficients in each level of decomposition
in [Matlab]
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From: Nyan Myo Naing on 8 Jul 2010 03:06 Dear All, I am wondering the wavelet decomposition implementation in Matlab. In wavelet decomposition using the command "wavedec", the number of coefficients in each level should be (length of original signal)/(2^j) where j = 1,2,3,....n For example, if the length of the original signal is 3600, it should be j = 1 -> 1800 j = 2 -> 900 j = 3 -> 450 j = 4 -> 225 j = 5 -> 112 But in matlab, number of coefficients are j = 1 -> 1804 j = 2 -> 906 j = 3 -> 457 j = 4 -> 233 j = 5 -> 121 Could sbd explain the discrepancy? Thanks
From: Nyan Myo Naing on 8 Jul 2010 03:37 Thanks, I know now. Bcz it goes by convolution. http://www.mathworks.es/access/helpdesk/help/toolbox/wavelet/ch01_i11.html Thanks "Nyan Myo Naing" <nyannmn(a)gmail.com> wrote in message <i13tct$hv$1(a)fred.mathworks.com>... > Dear All, > I am wondering the wavelet decomposition implementation in Matlab. > In wavelet decomposition using the command "wavedec", the number of coefficients in each level should be > (length of original signal)/(2^j) where j = 1,2,3,....n > For example, if the length of the original signal is 3600, it should be > j = 1 -> 1800 > j = 2 -> 900 > j = 3 -> 450 > j = 4 -> 225 > j = 5 -> 112 > > But in matlab, > number of coefficients are > j = 1 -> 1804 > j = 2 -> 906 > j = 3 -> 457 > j = 4 -> 233 > j = 5 -> 121 > > Could sbd explain the discrepancy? > Thanks
From: Wayne King on 8 Jul 2010 05:53 "Nyan Myo Naing" <nyannmn(a)gmail.com> wrote in message <i13tct$hv$1(a)fred.mathworks.com>... > Dear All, > I am wondering the wavelet decomposition implementation in Matlab. > In wavelet decomposition using the command "wavedec", the number of coefficients in each level should be > (length of original signal)/(2^j) where j = 1,2,3,....n > For example, if the length of the original signal is 3600, it should be > j = 1 -> 1800 > j = 2 -> 900 > j = 3 -> 450 > j = 4 -> 225 > j = 5 -> 112 > > But in matlab, > number of coefficients are > j = 1 -> 1804 > j = 2 -> 906 > j = 3 -> 457 > j = 4 -> 233 > j = 5 -> 121 > > Could sbd explain the discrepancy? > Thanks Hi Nyan, It has to do with the length of the filter and the setting for boundary value replication. The default mode for boundary value replication is symmetric half-point extension. You will notice that changing the length of the wavelet filter will increase the number of coefficients. x = randn(3600,1); wf = 'sym4'; [Ca,Cd] = dwt(x,wf); length(Ca) wf = 'sym8'; [Ca,Cd] = dwt(x,wf); length(Ca) The wavelet filter has increased in length by 4 and the number of coefficients has also increased by 4. If you wish to see the behavior you expected, you can set the dwtmode to periodization. dwtmode('per') Wayne
From: Nyan Myo Naing on 8 Jul 2010 23:36 Thanks Wayne "Wayne King" <wmkingty(a)gmail.com> wrote in message <i1476f$2p4$1(a)fred.mathworks.com>... > "Nyan Myo Naing" <nyannmn(a)gmail.com> wrote in message <i13tct$hv$1(a)fred.mathworks.com>... > > Dear All, > > I am wondering the wavelet decomposition implementation in Matlab. > > In wavelet decomposition using the command "wavedec", the number of coefficients in each level should be > > (length of original signal)/(2^j) where j = 1,2,3,....n > > For example, if the length of the original signal is 3600, it should be > > j = 1 -> 1800 > > j = 2 -> 900 > > j = 3 -> 450 > > j = 4 -> 225 > > j = 5 -> 112 > > > > But in matlab, > > number of coefficients are > > j = 1 -> 1804 > > j = 2 -> 906 > > j = 3 -> 457 > > j = 4 -> 233 > > j = 5 -> 121 > > > > Could sbd explain the discrepancy? > > Thanks > > Hi Nyan, It has to do with the length of the filter and the setting for boundary value replication. The default mode for boundary value replication is symmetric half-point extension. You will notice that changing the length of the wavelet filter will increase the number of coefficients. > > x = randn(3600,1); > wf = 'sym4'; > [Ca,Cd] = dwt(x,wf); > length(Ca) > wf = 'sym8'; > [Ca,Cd] = dwt(x,wf); > length(Ca) > > The wavelet filter has increased in length by 4 and the number of coefficients has also increased by 4. > > If you wish to see the behavior you expected, you can set the dwtmode to periodization. > > dwtmode('per') > > Wayne
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