For example, your boss ordered you to work, but you went downstairs to play billiards. Later, the boss found out, he was very angry and slapped you (note, this is the input signal, pulse), so your face Gradually (cheaperly) a bag will swell up, your face is a system, and the swelled bag is the response of your face to a slap, okay, so it establishes a meaningful connection with the signal system. A few more assumptions are needed to ensure the rigor of the argument: assume that your face is a linear time-invariant system, that is, whenever the boss slaps you, it hits you in the same place in the face (which seems to require your face to be enough Smooth, if you say that you have a lot of pimples, and even the whole face is continuous everywhere, it is too difficult, I have nothing to say haha), your face will always be in the same time interval Bulge a bag of the same height, and assume the size of the bulged bag as the system output. Well, then, let's enter the core content - convolution!
If you go underground and play billiards every day, the boss will slap you every day, but after the boss slaps you, your swelling will subside in 5 minutes, so after a long time, you will even get used to this kind of life ...If one day, the boss can't bear it anymore and starts the process of slapping you continuously at 0.5 second intervals, then the problem will come. The swelling of the bag that you slapped for the first time has not disappeared, and the second slap will come. , the bag on your face may bulge twice as high, the boss keeps slapping you, the pulse continues to act on your face, the effects continue to superimpose, so that these effects can be summed up, and the result is the height of the bag on your face A function that changes with time (pay attention to understanding); if the boss is more aggressive, the frequency is getting higher and higher, so that you can't distinguish the time interval, then the summation becomes an integral. It can be understood in this way, at a certain moment in the process, what does the degree of bulging of the bag on your face have to do with? It's about every time I hit you before! However, the contribution of each time is different. The earlier the slap, the smaller the contribution, so that is to say, the output at a certain time is the superposition of the previous input multiplied by the respective attenuation coefficients to form the output of a certain point. , and then put the output points at different times together to form a function, which is convolution. The function after convolution is the function of the size of the bag on your face changing with time. Originally, your bag can be swollen in a few minutes, but if you use it continuously, it will not go away for a few hours. Isn't this a smoothing process? Reflected in the formula of Cambridge University, f(a) is the a-th slap, g(xa) is the effect of the a-th slap at the x moment, and it is ok to multiply it and then superimpose it. Do you think this is the truth? I think this example is very vivid. Do you have a more specific and profound understanding of convolution?