What Are Wavelets | Understanding Wavelets, Part 1
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- čas přidán 21. 08. 2024
- This introductory video covers what wavelets are and how you can use them to explore your data in MATLAB®. Learn two important wavelet transform concepts: scaling and shifting. These concepts can be applied to 2D data such as images.
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Video Transcript:
Hello, everyone. In this introductory session, I will cover some basic wavelet concepts. I will be primarily using a 1-D example, but the same concepts can be applied to images, as well. First, let's review what a wavelet is. Real world data or signals frequently exhibit slowly changing trends or oscillations punctuated with transients. On the other hand, images have smooth regions interrupted by edges or abrupt changes in contrast. These abrupt changes are often the most interesting parts of the data, both perceptually and in terms of the information they provide. The Fourier transform is a powerful tool for data analysis. However, it does not represent abrupt changes efficiently.
The reason for this is that the Fourier transform represents data as sum of sine waves, which are not localized in time or space. These sine waves oscillate forever. Therefore, to accurately analyze signals and images that have abrupt changes, we need to use a new class of functions that are well localized in time and frequency: This brings us to the topic of Wavelets. A wavelet is a rapidly decaying, wave-like oscillation that has zero mean. Unlike sinusoids, which extend to infinity, a wavelet exists for a finite duration. Wavelets come in different sizes and shapes. Here are some of the well-known ones. The availability of a wide range of wavelets is a key strength of wavelet analysis.
To choose the right wavelet, you'll need to consider the application you'll use it for. We will discuss this in more detail in a subsequent session. For now, let's focus on two important wavelet transform concepts: scaling and shifting. Let' start with scaling. Say you have a signal PSI(t). Scaling refers to the process of stretching or shrinking the signal in time, which can be expressed using this equation [on screen]. S is the scaling factor, which is a positive value and corresponds to how much a signal is scaled in time. The scale factor is inversely proportional to frequency. For example, scaling a sine wave by 2 results in reducing its original frequency by half or by an octave. For a wavelet, there is a reciprocal relationship between scale and frequency with a constant of proportionality. This constant of proportionality is called the "center frequency" of the wavelet. This is because, unlike the sinewave, the wavelet has a band pass characteristic in the frequency domain. Mathematically, the equivalent frequency is defined using this equation [on screen], where Cf is center frequency of the wavelet, s is the wavelet scale, and delta t is the sampling interval. Therefore when you scale a wavelet by a factor of 2, it results in reducing the equivalent frequency by an octave.
For instance, here is how a sym4 wavelet with center frequency 0.71 Hz corresponds to a sine wave of same frequency. A larger scale factor results in a stretched wavelet, which corresponds to a lower frequency. A smaller scale factor results in a shrunken wavelet, which corresponds to a high frequency. A stretched wavelet helps in capturing the slowly varying changes in a signal while a compressed wavelet helps in capturing abrupt changes.
You can construct different scales that inversely correspond the equivalent frequencies, as mentioned earlier. Next, we'll discuss shifting. Shifting a wavelet simply means delaying or advancing the onset of the wavelet along the length of the signal. A shifted wavelet represented using this notation [on screen] means that the wavelet is shifted and centered at k. We need to shift the wavelet to align with the feature we are looking for in a signal.The two major transforms in wavelet analysis are Continuous and Discrete Wavelet Transforms. These transforms differ based on how the wavelets are scaled and shifted. More on this in the next session. But for now, you've got the basic concepts behind wavelets.
Probably the best short and concise explanation of wavelets I have seen, well done
The best explanation ever... Really professional video. Lecturer doesn't appear professor-like, but give this guy just one minute, and you will see he is the best professor ever. I watched following videos as well. This saves time. In 4 minutes you learn more than reading the same thing in book for 40 minutes, or watching lesser quality video for 20 mins.
A lot of thinking and care has gone into the making of this wavelet video series, and it shows. The explanations are clear and to the point. thanks for the post @Kirti Devleker
Extraordinary! Great respect (university teacher here). I have a lot to learn from your teaching tehniques!
All set in less than 5 min, very well explained.
Clear, concise, and straight-forward. Thank you.
This is a very helpful overview for every researcher working on the data analysis. Thank you for this session..
Really professional, clear and informative. Thank you !
This is how to properly teach an advanced topic. Start with the very basics. Very well done sir. Upvoted.
CLEARLY UNDERSTOOD SIR. THANK U SO MUCH
Never saw such a clever way to describe wavelengths. E
Well done!
02:39 - Sorry, shouldn't the graphics of the frequency be shift between up and bottom?
So Precise yet so clear sir. Thanks !
You explain the concept well clearly.
The best introductory video to wavelets.! Thank you very much.
Concise explanation of Wavelet. Good effort.
You explained it way better than my teacher.
Very precise and well explained. Thank you.
Thanks, exactly what I needed for my artificial vowel project
fun pp (-':
Great, simple and concise!
This guy is REALLY good!
OMG best wavelet explanation... bae .... 😍 😍 😍 😍
really easy and precise explaination. thank you.
Ultimate & Excellent presentation on...introduction to the Wavelets..Thank you..Sir
Very well explained!
Thank you very concise . Helped a lot
Great introduction! Thank you!
Thank you for your explanation
Nice job, thanks for this explanation!
Great intro.. Thank you.. Can i know what tool did you use for the animation?
whiich will be good for emg signals either fourier r wavelet transforms
Thank you! great introduction
bless your soul
Great sir, very nice and simple explanation
Great Explanation..Thank you....!!!
What prerequisite knowledge do i need to understand this? I don't really know what you're talking about, but I want to know...
edit: To clarify, what math concept(s) do I need to learn first? What discipline(s) of math? I've completed basic calculus so far.
This uses a lot of stuff I learned in my signals & systems course (specifically taking a real time signal and putting it in frequency domain with fourier, and function manipulation)
Nicely explained 👍
Fantastic! :) Many thanks!
Why is the equation Ψ(x/s)s=y? This seems to imply that the wavelet is made taller vertically when it is squished together horizontally. Yet your animation doesn't show this happening...
Am I missing something? Why isn't it Ψ(x/s)=y?
very good.I enjoyed
Excelent video. congratulations
Hello. Very Well Donne for the Clarity and Simplicity of your lesson! (y) (y) (y)
Very good explination
Sir I have a doubt . If a wavelet transform is continues means are we perform transformation on continuous time signal or if a wavelet transform is DWT is it means we are performing wavelet transform on Discrete time signals . Please clarify my doubts.
Thank you very much
Great! Thank you so much.
So wavelets help get the localization aspect into creating a given signal.
From that time -scale representation how we will obtain the frequency of our given signal??
Hi, I have a question about wavelets: I want to analyse power system fault currents with wavelet. when I use 1-d wavelet toolbox, d1 to d5 coefficients are in the same time scale and I can for example find the value of each coefficient in a specific milisecond like 2.05. but when I use "wavedec and detcoef" in my mfiles, the d1 to d5 coefficients are not in the same x axis time scale. for example if my wave exported from PSCAD be a matrix of 1000 samples, d5 will be 500 samples, to d1 will be 20 samples for example. and they cannot be synced plotting together finding all coefficients in a certtain x axis like time, which is being plotted automatically in 1-d dwt toolbox. so whats wrong with my understanding or using of wavelets? thanks
Vevvlets ! thanks mate !
OMG I want that swaggy MathWorks shirt sooo baaad
Thank you.
Amazing!!!
What is best between filters and wavelets for denoising
very good ..gettig interested
I don't understand how wavelets circumvent the problem arising from the sine waves oscillating for infinite time and space. Aren't those wavelets composed of infinite sine waves?
Also why at 3:00 are we dividing by the sampling interval?
how to define j for scaling?
how high are you????
Great video for post weed high!!!
Don't like your own comments.
420
Can u tell me exactly wavelet filter. Video was very nice
Dumb question here - what does ψ mean in 2:15 ?
Stuntkoala it's just a letter wich represents the signal. like the letter f stands for function in analysis.
amazing
Good morning sir,
i wnat to pdf formate of wavelet transform and wavelet cosine transform and its application .
please provide me because my exam is near.
At this time their subs and view of this video are equal
Please Explain contourlet wavelet Transform
Can we have a wavelet of single frequency!!??
How to get elliot wave automated software plz suggest anyone
If the public actually cared about Wavelets, they would be outraged that there is a wavelet called the "Mexican Hat". Actually funny.
We live in a truly cucked society
几乎每句话都值得记笔记，讲的很好，可是没有人觉得他口音太太太重了吗，好多单词听了几十遍也听不懂 是我英语太差了？。。。
有字幕
Hey could you try this software? Encounter: 'Circuit Solver' by Phasor Systems on Google Play.
I love India
Nice presentation! But the person, why so serious :/ :P
I love my dear friend
are you an Indi?
vavelets
There's something better for signal analysis.
(Disclaimer: I have invented one).
So what's the better method? Post a link or something to your work ...
@@riskyrisk663 thanks. I have a number of demo videos right on my channel; more on trotsenko.com.ua
I currently demo it talk about it, but not disclose it yet.
Your explanation is too fast
complete bullshit HE IS LOOKING LIKE A ZOMBIE