How to cover all spectrum in wavelet when it which is behalved?

Question

As I know , wavelet decomposition behave with halve. I mean that a way like this HH HL LH LL.

But I wonder, how to corver the all spectrum when it was halved? I think if it want to all cover spectrum then it might be needed infinity halve.

How can cover all the spectrum?

themantalope · Accepted Answer · 2015-05-07 06:53:31Z

1

It is covered - its just the signal that is the residual part of what you didn't filter yet.

answered May 7 '15 at 6:53

themantalope

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$\begingroup$ Would you please let me know more? Does it just remain residual ? I don't understand. Because that way is not cover aren't you? $\endgroup$ – gmotree May 7 '15 at 13:42
$\begingroup$ The discrete wavelet generates "filter banks". After the first iteration, you are left with two signals - a signal that only contains frequencies from sampling rate/2 to sampling rate/4 Hz (this is the high frequency bank that you just filtered out) and another signal that only contains frequencies from sampling frequency/4 to zero Hz. If you have enough samples left in the low frequency bank, you can repeat the filtration process again - if you repeat again you will now be left with 3 signals. $\endgroup$ – themantalope May 7 '15 at 15:03
$\begingroup$ However, it should be noted that this is the case for discrete wavelet filtration - a process that uses "continuous" transform methods may achieve better frequency resolution within the filter banks. $\endgroup$ – themantalope May 7 '15 at 15:06
$\begingroup$ Thanks. But as you can said, that way need a cock. What if I havd enough decomposition then should I have to ignore or throw out the rest part? $\endgroup$ – gmotree May 7 '15 at 23:23
$\begingroup$ What do you mean by "need a cock"? $\endgroup$ – themantalope May 11 '15 at 14:56

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