Welcome to this introductory tutorial on wavelet transforms. The wavelet transform is a relatively new concept (about 10 years old), but yet there are quite a few. 30 May We basically need Wavelet Transform (WT) to analyze non-stationary signals, i.e. , whose frequency response varies in time. I have written that. The wavelet transform or wavelet analysis is probably the most recent solution to an interesting tutorial aimed at engineers by Robi Polikar from Iowa State.

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Wavelet Tutorial – Part 1

The Wavelet transform is a transform of this type. Note that the four peaks are well separated from each other in time.

Actually, here we calculate the discrete Fourier transform DFTin which case the frequency axis goes up to at least twice the sampling frequency of the signal, and the transformed signal is symmetrical. However, as far as the engineering applications are concerned, I think all the theoretical details are not necessarily necessary! This procedure is followed, until the end of the signal is reached by shifting the window with “t1” seconds intervals.

This pathological condition, however, may not always be quite obvious in the original time-domain signal.

The best we can do is to investigate wavslet spectral components exist at any given interval of time. Futorial frequency spectrum of a signal shows what frequencies exist in the polikaf. It follows that no matter where in time the component with frequency “f” appears, it will affect the result of the integration equally as well. These will correspond to three different FTs at three different times. The reason of the noise like thing in between peaks show that, those frequencies also exist in the signal.


I have just noticed that I have mistyped it. For example the publication frequency of a daily newspaper is higher than that of a monthly magazine it is published more frequently. The top plot in Figure 1. In this tutorial I will try to give basic principles underlying the wavelet theory. There are number of transformations that can be applied, among which the Fourier transforms are probably by far the most popular.

For example, if we take the FT of the electric current that we use in our houses, we will have one spike at 50 Hz, and nothing elsewhere, since that signal has only 50 Hz frequency component.

To make a long story real short, we are faced with the following dilemma:. When I first started working on wavelet transforms I have struggled for many hours and days to figure out what was going on in this mysterious world of wavelet transforms, due to the lack of introductory level text s in this subject.

Wavelet Tutorial – Part 1

Interpret the above grid as follows: Contrary to the signal in Figure 1. Should you find any inconsistent, or incorrect information in the following tutorial, please feel free to contact me.

Note that the Fourier transform tells whether a certain frequency component exists or not. In the following tutorial I polokar assume a time-domain signal as a raw signal, and a signal that has been “transformed” by any of the available mathematical transformations as a processed signal.


This will show us which frequencies exist at which time there is an issue, called “uncertainty principle”, which states that, we cannot exactly know what frequency exists at what time instancebut we can only know what frequency bands exist at what time intervalsmore about polukar in the subsequent parts of this tutorial. Therefore, the integral in 1tutorizl calculated for every value of f. The answer, of course, is application dependent: We know which signal corresponds to which frequency band, and if we put all of them together and plot them on a 3-D graph, we will have time in one axis, frequency in the second and amplitude in the third axis.


The FT of both of the signals would be the same, as shown in the example in part 1 of wavelef tutorial.

wavepet Every transformation technique has its own area of application, with advantages and disadvantages, and the wavelet transform WT is no exception. In this signal, there are four frequency components at different times. Furthermore, in order to obtain the stationarity, we have to have a short enough window, in which the signal is stationary.

The Wavelet Tutorial

However, if this is not the case, then a good window function, could be more difficult than finding a good stock to invest in. As we will see soon, the answer depends on the particular application, and the nature of the signal in hand. How wavelet transform works is completely a different fun story, and should be explained after short time Fourier Transform STFT.

However, I would like to mention a couple important points again for two reasons: The following turorial shows four window functions of varying regions of support, determined by the value of a. In other words, when we plot the signal one of the axes is time independent variableand the other dependent variable is usually the rogi.