The following are preliminary understandings
The origin of convolution:
Convolution is an operation method whose purpose is to better obtain the output signal at a time point in a linear time-invariant system. (++ Forgive me, I don't know the origin and background of this very well)
I heard a story that the boss took a bunch of input signal functions and asked Zhang San to draw the waveform of the output signal, and the method was to differentiate the input signal into countless small pulses, input them into the system, and the superimposed result is the output Signal (integration), this operation method is convolution.
What is convolution:
For example (taken from Zhihu for easy understanding):
The main idea of the first version: play the game, magic damage, hit once, continue to lose blood every second, last for five seconds, the blood loss at 0s is 1, 2, 3, 4, 5
And one hit is the unit signal x[k], that is, when k=0, x(k)=1, the obtained response (blood consumption and time function image) is h(n), and hitting again in the 2s to lose blood is 1, 2, 3, 4, 5, at this time k=2
Then the response obtained is h(n-2), then the 0s and 2s are played, that is, x[k]=0,2, the blood loss becomes 1, 2, 4, 6, 3, 4, the image as follows:
Then the accumulation function for arbitrary attacks is
is the convolution formula
Second version to the effect:
(repair)
self-understanding:
(repair)
What kind of problem to solve:
To be honest, when I roughly look at the textbook, it is not clear what convolution is for, that is, what is the use? Is it to ask for the output at a certain time?
The physical meaning is as follows:
The principle is to decompose the signal into the sum of the impulse signals, and solve the zero-state response of the system to any excitation signal with the help of the system's impulse response h(t).
According to the above understanding, the output signal is obtained through the system by means of the difference of the input signal. And the condition of this convolution is only for linear time-invariant systems,
What is linear time-invariant, that is, at any time, the function changes corresponding to the input and output are consistent.
What goes up and what goes down (supplement)
After that, there are examples and some exercises in Chapter 2, and then we talk about understanding.