Reprinted "Introduction to mantan Signals and Systems"

A good article. I hope everyone will like it. I really appreciate the last few words!

 

Reprinted: Introduction to Signals and Systems-Lesson 1 What is convolution? What is Fu Liye transformation? What is Laplace transformation introduction?

 

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Many of my friends, like me, have learned a bunch of signal courses for electronics majors in Engineering. I have not learned anything. I took the test on the formula and then graduated.

Let's talk about the question "What is the use of convolution. (Someone replied that "convolution" exists in the subsequent sections of the course "signal and system. I yelled at him and took him out !)

Tell a story:

John has just been hired as a tester for an electronic product company. He has never taken the "signal and system" course. One day, he got a product. The developer told him that the product has an input end and an output end. A limited input signal only produces a limited output.

Then, the manager asked Michael to test what kind of waveform The product outputs when the sin (t) (T <1 second) signal is input (with a signal generator. Three photos were taken and a waveform chart was taken.

"Good! "Said the manager. Then the manager gave a heap of A4 paper: "There are thousands of signals. The formula shows that the duration of the input signal is also determined. Test the Output Waveforms of the following products respectively! "

Now, Michael is in his mind. "God, help me. How can I draw these waveforms? "

So God came up: "James, you only need to perform a test and draw the Output Waveforms corresponding to all input waveforms in a mathematical way ".

God went on to say, "To give the product a pulse signal, the energy is one second, and the output waveform is shown! "

James took care of it. "What then? "

God said, "For an Input Waveform, you imagine dividing it into countless small pulses and inputting it to the product. The result of the superposition is your output waveform. You can imagine that these small pulses lined up into your product. Every time you generate a small output, when you draw a timing diagram, the waveform of the input signal seems to be in turn into the system. "

James learned: "Oh, the output results are all points! Thank God. What is the name of this method? "

God said, "convolution! "

From then on, James's work was much easier. Every time the manager asks him to test some signal output results, James only needs to make calculus on A4 paper to submit the task!

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James worked happily until one day, and his peaceful life was broken.

The manager took a small electronic device and connected it to the oscilloscope and said to James, "Look, the waveforms produced by this small device cannot be described by a simple function. Moreover, it continuously sends signals! But fortunately, this continuous signal repeats every other time. John, let's test the following output waveforms when connected to our devices! "

Zhang San waved his hand: "the input signal has no time limit. Do I have to test the infinite time to obtain a stable and repeated waveform output? "

The manager is angry: "You can fix it for me, or you may have fired the squid! "

Zhang sanzhi thought: "this time, the input signal is connected to the formula, and a chaotic waveform. The time is infinitely long, And the convolution cannot work. What should I do? "

In time, God appeared again: "ing chaotic time domain signals to another mathematical domain, and ing back after computation is complete"

"Every atom in the universe is rotating and oscillating. You can regard the time signal as a combination of several vibrations, that is, something that can be determined and has a fixed frequency. "

"I will give you a mathematical function f, with infinite input signals in the time domain limited in the f domain. Chaotic input signals in the time domain are neat and easy to see in the f domain. In this way, you can calculate"

"At the same time, the convolution of the time domain in the f domain is a simple multiplication relationship. I can prove it to you"

"After a limited program is computed, you get an output waveform after the F (-1) inversion is returned to the time domain, and the rest is your mathematical computation! "

James thanked God and kept his job. Later, he learned that the F-domain transformation has a name called Fu Liye. What is it ......

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Later, the company developed a new electronic product with an infinite length of output signal. This time, James started learning Laplace ......

Postscript:

It's not because the teaching materials are poor or the teachers are not good at learning.

I really appreciate Google's interview questions: I used three sentences, like the old lady, to explain what a database is. Such a proposition is very good, because we do not have a deep understanding of a proposition, and do not think carefully about the design philosophy of a thing, we will fall into the details of the mud: Back formulas, mathematical derivation, points, answer the question, but there is no time to answer "why ". What a university teacher cannot do is to "read thick books and thin books". He can't tell the philosophical truth, simply endorse and turn over PPT, and make boring mathematical proofs, then I blame "the current generation of students is not like a generation". What is the significance?