I went through university and this was way more understandable than whatever we were taught

It was submitted to the contest, but I already know I'm not in the top 100 lol

yea please , its awesome, and feels like a nice fresh breath =) edit : the last sound effect made me hit the bell button .

I love the background music as well, it helped me focus

Nice! I was actually thinking that if you treat use the fourier transform's discrete version, you can apply that to the convolution. You'll start to see the terms line up in a way that makes frequency multiply. I never expected it to connect back to question one.

I'm used to putting it on the left because I use "state space representation" of diffeqs a lot. Also, when you assign a variable when programming software, the variable you want to assign goes on the left, and therefore, when you model these equations in code the outputs go on the left.

@@sigfyg8384 Yeah. I like that notation because it reminds you that the matrix-vector product is just a vector. Or that a scalar product simplifies to a scalar value.

I also put it on the right, never seen otherwise. I study math in France

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

Brother I know mechanical engineers could find resonance but when I had a deep thought on this resonance Is an slow accumulation of energy which is accumulated very high in small installments when the frequencies match if you strike a turning fork of 50 hz you get the same frequency of vibration on another tuning fork so they both vibrate if you strike it harder the amplitude changes hence loudness is a human factor the frequency is the same the languages that human speak through out the world the sound only resonate your ear drum for few seconds my question is that the harmonics is the fundamental frequency and overtones are the frequency that follow it take a word in any language you spell it according to convolution the thing scales and ques and stack the signal so convolution can be used to model resonance so when your ear drum vibrates it vibrates so the electrical signals are carried to brain like tuning fork ear drums vibrate within the audible spectrum 20 hz to 20000 hz hence resonance is caused by the word we speak and within the audible range the ear drums vibrate and we make sense of words I have seen in one videos on KZfaq that due to harmonics in any sound causes resonance which could be modelled by convolution recalling the resonance its destructive because slow and steady accumulation of sound on the mass causes high stress and high energy to build inside and stress increase and the system fractures or collapses but our ear drum hearing the sound from human languages try to vibrate but why our ear drum when subjected to continuous exposure of sound does not fracture or rupture like a wine glass iam not telling about high loud sound higher than 80 db but a audible range sound within the frequency of 20 hz to 20000 hz under continuous exposure why it's not damaging it again not failure by high energy but low one in synchronisation on air . But I tried it in my students when I told them to be quite in class they did not listen to me so I took my phone and set an frequency 14000 hz and they told it was irritating the idea of resonance is "small effort but large destruction " just like Tacoma bridge where the wind just slowly accumulated energy on the bridge and it collapsed it so my conclusion is if an audible frequency at continuous exposure to an human ear can it cause bleeding again "small effort but great destruction" sorry for the long story I you are able to reach hear you must be as curious as me so still not finished the ear drum is shook by harmonics in the sound we make by the words( or )overtones in the sound we make by the words I know harmonics is the fundamental frequency and overtones are following it which under slow and steady accumulation of sound energy resonates and could damge the ear drums again "small effort but big destruction" not to mention we assume the person is in coma or brain dead hence when the sound irritates him he or she could not make a move so my question is so simple normally human ear responds to harmonics or overtones according to convolution which could be a disaster but with minimal effort 🙏🙏🙏🙏 at here I could be wrong because harmonics can also be used to construct sound so can it be destructive or the overtones which are the trouble makers and which one according to this gives a response curve when two signals convolved by harmonics or overtones which is destructive but with minimal effort and convolution happens when ear drums oscillate is by harmonics or the overtones or also the trouble makers there

The impulse function/response is b(t). You could call d(t) the total response, which is made up of many impulse responses.

f(-t) is f(t) but flipped around the vertical axis. f(t-1) is f(t) but shifted forward by one. Combine these two transforms, and you get f(-(t-1)), which is a flipped and shifted version of f(t). It's ok to be confused here. I suspect that the source of the confusion is trying to comprehend why the flip and the shift are not commutative. To see what I mean, compare f(-t-1) vs f(-(t-1)). f(-t-1) Flip first, Shift second f(-(t-1)) Shift first, Flip second When you switch the order of the transformations, you get two different results. Now you are thinking along the lines of Group Theory, where this question of commutating becomes important! Another note: I could've distributed the negative sign in and got f(-t+1) or f(1-t), but that makes it harder to see the flip and shift. Different representations of the same phenomena can tell two different stories. For example, a/b and a*(1/b) are mathematically equivalent, but they communicate two very different ideas. Similarly, f(-t+1) and f(1-t) don't communicate the idea I want to emphasize as clearly as f(-(t-1)).

It is not possible to receive cookies from the bakery on day 0 for a dollar you give on day 4, UNLESS the bakery can predict the future. Last I checked, bakeries do not have divination powers, so c(0) cannot depend on b(-4). Since the impulse response b(t) get's flipped around to b(-t), the negative sign actually refers to a point in the future. The LATEST part of the impulse response interacts with the EARLIEST part of the input signal, which is why you need the flip.

I might have a new one ready by the end of December.

What do you mean by "different form"? The addition 1+1 = 2 is technically a matrix multiplication of the vectors [1, 1] and [1, 1] transposed (so a 1x2 times a 2x1). Does this mean that 1+1=2 is just matrix multiplication but in a "different form"? Now, that's not a convenient way to represent 1+1=2, but in other scenarios turning something into a matrix multiplication is super useful. So matrix multiplication isn't really a "form" as much as it is a representation. Here's a blogpost I wrote that digs into this some more: sigfyg.medium.com/the-philosophy-of-linear-algebra-ac2d9ce14619

@@sigfyg8384 thank you for the material!

c(0) is supposed to be d(t).b(-t), as shown in the video. At t=0, the only part of the input d(t) that can have any impact on the output is d(0). When you suggest that c(0) should be d(t).b(-(t-6)), that means the system is somehow reading signals from the future!

@@sigfyg8384 Yeah, I guess i got confused because you said you took the rows of the matrix to determine c(t) so for c(0) you use the first row which is b(-(t-6)) and for c(6) you use b(-t).

Look up "state space representation". The derivative vector, which is the product of a matrix and the state vector, is written on the left side.

Furthermore, when assigning a variable in software the variable you want to assign goes on the left. Therefore, if you want to write matrix multiplications in code, your output goes on the left.