Convolution vs. Correlation in Signal Processing and Deep Learning [DSP #10]

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In this video, we are discussing the definition of correlation and main differences between correlation and convolution.
Fast convolution explained: • Fast Convolution: FFT-...
In case of any doubt in understanding, please, refer to the article above 🙂
00:00 Introduction
00:18 Motivation
00:49 Convolution definition
01:07 Correlation definition
02:06 Crosscorrelation with an example
02:48 Autocorrelation with an example
03:28 Main difference between convolution and correlation
04:11 Correlation computed using convolution
04:55 Applications of correlation via convolution formula
05:55 Summary
#dsp #correlation

[@WolfSoundAudio]

Have I helped you with this video? If yes, please, consider buying me a ☕ coffee at www.buymeacoffee.com/janwilczek
Thanks! 🙂

[@AzeezAbass]

You videos are always so straight forward insightful. IMO, best DSP content on the internet. Thank you.

[@fernandozolubaspreto6976]

Thanks for the high-quality content. It helps me a lot to understand these two concepts and how to use them.

[@WolfSoundAudio]

Thanks for sharing!

[@mahmoodmohanad4726]

Great explanation, best video about correlation on youtube

[@ejkitchen]

Fantastic video and the best explanation I have seen so far. Your visuals and animations are also very well done. I just bought you a coffee.

[@WolfSoundAudio]

Thank you so much, Eric! I am happy you benefited from the video!

[@luciasevillarodriguez9032]

very useful video, thamk you very much!!

[@torond6908]

Great pointers to further reading and connected ideas!

[@WolfSoundAudio]

Thank you, I'm glad you liked it!

[@achrafeleuch4276]

best explaination

[@ranam]

Telling the application of convolution in terms of signal processing may help a part of people in the telecommunication and eee engineers but when convolution meets signal processing it also is used as a filter but my question is I have read convolution even it's useful for mechanical engineers such that in resonance when a failure occurs not due to massive force hitting an object results in large deformation could cause failure or an large impulsive force acting on it for a duration of time could cause failure but there is an another phenomenon where the natural frequency of any object is reached the energy builds in it very high and could cause a failure in this manner a small disturbance which accumulates over a time and causes a high energy to build in the system due to energy very high it causes stress and the system collapses this is highly different from stability perspective of control system being not stable does not mean it's accumulating energy inside it but in case of amplifier there is an capacitor or inductance device which causes the attenuation in the electrical signal and filters some frequencies but in other perspective amplifier amplifies the signal such that it stack ques and scales the signal but I don't know this is done by capacitor or am inductor but convolution is useful to both mechanical civil eee ece and every applied scientist and engineers hence it's used as a filter in an circuit or used to amplify but even transistor amplifies the signal without an capacitor or an inductor I guess also mechanical engineers can use it to model resonance hence the energy inside the system build high by periodic accumulation of the system reaching its natural frequency which leads to failure and I can also tell you that when amplifier filter or amplifies the signal it used convolution hence it's useful to every applied scientist and engineers but not to mention the pure Mathematicians use it of convolution of kernels thankyou guys some of my inference could be wrong if somebody or the author of the video is familiar with it please correct the above and educate me thank you for the wonderful video sir

[@arash4232]

Thanks so much.
I was waiting to hear why we flip one of the signals in convolution. What is that for?

[@assalaassala2973]

Thanks

[@WolfSoundAudio]

You're welcome! Glad you enjoyed it :)

[@chakib2378]

Thank you for yout video. I have a question, you said that we can compute convolution and modify it in order to have the correlation but what is the point of doing this ? Actually it seems faster to compute the correlation than the convolution (because there is no extra flipping to do). So why compute convolution in order to get correlation whereas computing directly the correlation seems to be faster ?

[@jemussi7842]

Thanks for the video. I have noticed some people including lecturers on youtube incorrectly using the terms interchangeably. You said you can flip the output of convolution to get correlation but looking at the plots @ 3:55 they are not mirror images. However if you do a vertical then horizontal flip or rotate 180 degrees about the origin of one signal they match. Is this what you mean?

[@WolfSoundAudio]

Thank you very much for the question! Indeed, the terms are used interchangeably while they shouldn't be.
As for your question: is obtaining correlation out of convolution a simple visual transform of a plot? Definitely not. Here, your observation is true: the correlation at 3:55 is simply a rotation of the convolution. However, it is true only because for one of the signals involved (two periods of the sine), x[n], it holds that x[-n] = -x[n]. If you look at the formula around 4:24 , you'll see that this allows us to obtain correlation by simply flipping the output of convolution vertically and negating it.
Is it clear, why is your observation true here but not true in general?
Thank you once again for your input, probably other people ask themselves the same question.

[@arash4232]

Hi,
I have senses about correlation but I cant understand the benefit of flip in convolution; what is that for?

[@Shiny_Mewtwo]

I will buy you a dinner when I got a job in the future🤣

[@WolfSoundAudio]

Haha, ok!