QuoteOriginally posted by: blackscholesI'm back. I did some more reading. I found a Wavelet Tutorial by Robi Polikar. I understand everything until this graph and I think this is where I need to make the connection.The top graph is the original signal and the bottom graph is the DWT coefficients after the transform was applied. Here is the verbiage from the website :"The frequency bands that are not very prominent in the original signal will have very low amplitudes, and that part of the DWT signal can be discarded without any major loss of information, allowing data reduction. Figure 4.2 illustrates an example of how DWT signals look like and how data reduction is provided. Figure 4.2a shows a typical 512-sample signal that is normalized to unit amplitude. The horizontal axis is the number of samples, whereas the vertical axis is the normalized amplitude. Figure 4.2b shows the 8 level DWT of the signal in Figure 4.2a. The last 256 samples in this signal correspond to the highest frequency band in the signal, the previous 128 samples correspond to the second highest frequency band and so on. It should be noted that only the first 64 samples, which correspond to lower frequencies of the analysis, carry relevant information and the rest of this signal has virtually no information. Therefore, all but the first 64 samples can be discarded without any loss of information. This is how DWT provides a very effective data reduction scheme."I don't quite get how all but the first 64 samples can be discarded without any loss of information. I understand that the first 64 DWT coefficients are prominent but how does that correspond with the first 64 samples of the original signal from the first graph. Most of the information is in the middle part of the signal.Any clue?The "first 64 samples" of the DWT are the lower frequency components of the ENTIRE time domain (not just of the first samples of the original signal). The original signal contains a relatively low-frequency object (of about 0.09 samples/cycle). Thus, there's little information in the DWT coefficient in highest-frequency coefficients 129-256 (= 0.5 samples/cycle) or the second-highest frequency coefficients 65-128 (= 0.25 samples/cycle). Most of the information is in coefficients 33-64 (= 0.125 samples/cycle), and coefficients 17-32 (= 0.0625 samples/cycle).Although each DWT coefficient might have some correspondence to a subarea of time domain signal, it's not a simple relationship like "the first 64 DWT coefficients correspond with the first 64 samples of the original signal."To really understand what's going on, I strongly recommend you generate some signals, run the DWT and look at how the DWT coefficients change when you change the shape of your signal, scale it wider and narrower, or move it earlier or later in time.