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Pywavelets applied to time series

For DWT, the original signal is downsampled by a factor of two at each level of decomposition. It's based on filter banks, in which data is downsampled by a factor of 2, i.e., by a low pass filter - ...
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For continuous systems that in Quasi-static / Static Equilibrium are Memoryless?

@Tim Wescott's answer is already addressing this issue but, if you still have problems with it then why not concoct a test case and see, practically, what happpens when you're removing the states? ...
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