THE WAVELET TUTORIAL. PART IV by. ROBI POLIKAR. MULTIRESOLUTION ANALYSIS: THE DISCRETE. WAVELET TRANSFORM. Why is the Discrete. ROBI POLIKAR Abstract: The theory and applications of wavelets have undoubtedly dominated the wavelet transform is rapidly gaining popularity and rec-. WAVELET ANALYSIS. The Wavelet Tutorial. by. ROBI POLIKAR ยท Also visit Rowan’s Signal Processing and Pattern Recognition Laboratory pages.

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If this variable does not change at all, then we say it has zero tutofial, or no frequency. There are other transforms which give this information too, such as short time Fourier transform, Wigner distributions, etc.

Today Fourier transforms are used in many different areas including all branches of engineering. To make a real long story short, we pass the time-domain signal from various highpass and low pass filters, which filters robj either high frequency or low frequency portions of the signal. For the signal in Figure 1.

### Wavelet Tutorial – Part 1

If something a mathematical or physical variable, would be the technically correct term changes rapidly, we say that it is of wwavelet frequency, where as if this variable does not change rapidly, i.

The first one is a sine wave at 3 Hz, the second one at 10 Hz, and the third one at 50 Hz. There are number of transformations that can be applied, among which the Fourier transforms are probably by far the most popular.

Then we take the lowpass portion again and pass it through low and high pass filters; we now have 4 sets of signals corresponding to Hz, Hz, Hz, and Hz.

The bottom oolikar however, corresponds to low frequencies, and there are less number of points to characterize the signal, therefore, low frequencies are not resolved well in time. This means that if you try to plot the electric current, it will be a sine wave passing through the same point 50 times in 1 second.

For example the electric power we use in our daily life in the US is 60 Hz 50 Hz elsewhere in the world. Take a look at the following grid:. The natural question that comes to mind is that is it necessary to have both the time and the frequency information at the same time?

Note the four spectral components corresponding to the frequencies 10, 25, 50 and Hz. In the following tutorial I will assume a time-domain signal as a raw signal, and a signal that has been “transformed” by any of the available tuotrial transformations as a processed signal.

In other tuttorial, when we plot the signal one of the axes is time independent variableand the other dependent variable wavflet usually the amplitude. Both of them show four spectral components at exactly the same frequencies, i. Now, compare the Figures 1.

### INDEX TO SERIES OF TUTORIALS TO WAVELET TRANSFORM BY ROBI POLIKAR

Should you find any inconsistent, or incorrect gutorial in the following tutorial, please feel free to contact me. That is, no frequency information is available in the time-domain signal, and no time information is available in the Fourier transformed signal. In discrete time case, the time resolution of the signal works the same as above, but now, the frequency information has different resolutions at every stage too.

So how do we measure frequency, or how do we find the frequency content of a signal? Note that rkbi plots are given in Figure 1. The concept of the scale will be made more clear in the subsequent sections, but it should be noted at this time that the scale is inverse of frequency.

Intuitively, we all know that the frequency is something to do dobi the change in rate of something. You will find an e-mail at the bottom of this page. One word of caution is in order at this point.

In these cases it may be very beneficial to know the time intervals these particular spectral components occur. Let’s give an example from biological signals. The uncertainty principle, originally found and formulated by Heisenberg, states that, the momentum and the position of a moving titorial cannot be known simultaneously.

Consequently, the little peak in the plot corresponds to the high frequency components in the signal, and the large peak corresponds to low frequency components which appear before the high frequency components in time in the signal. However, interested readers will rogi directed to related references for further and in-depth information.

## Wavelet Tutorial – Part 1

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.

Therefore, FT is not a suitable technique for non-stationary signal, with one exception: In this document I am assuming that you have no background knowledge, whatsoever. The following shows the FT of the 50 Hz signal: That is, high scales correspond to low frequencies, and low scales correspond to high frequencies. Although FT is probably the most popular transform being used especially in electrical engineeringit is not the only one. For a better understanding of the need for the WT let’s look at the FT more closely.

The frequency spectrum of a signal shows what frequencies exist in the signal. Note however that, it is the good scale resolution that looks good at high frequencies low scalesand good scale resolution means poor frequency resolution and vice versa. Often times a particular spectral component occurring at any instant can be of particular interest.