Thoughts on reading Fourier series

To be honest, the Fourier series is really quite powerful. However, the people who think of this thing is very strong, it is clear that the white people are also very powerful, the only thing that is not bad is that the people who designate our teaching materials and learn these materials come out of their own thinking they have mastered these content but actually do not understand the person.

Well, in fact, I had to see the image from two dimensions in the time domain and frequency domain to find feature points, I was blinded, until now have to face him. (Forget it, maybe this is the verdict ...) ）

The above are all spit grooves. If I want to read the Fourier transform, I feel that I have read some of the notes here before I go to see, people's articles may be better. Address: http://blog.jobbole.com/70549/

The image can be described from two dimensions: one is the time domain and the other is the frequency domain.

The beautiful melody you hear can be described from two dimensions:

One, one is the score. "It's not appropriate.

One thing can be described from two dimensions:

The node in which the event occurred, such as the traffic police you saw in the penalty of speeding. This is the image you see, and one of the reasons why it is common to cause events. (a bit like the inevitable coincidence of the theory of Marxism.) The punishment must satisfy two things: the traffic policeman is present, the car is speeding.

Another example: Eat steamed bread of that example: you eat full is a node, a result, you say ah, if I would eat the nineth one. But in fact, you eat full of this thing is by 9 steamed bread co-led. They are more like the cause and effect of the inevitable, you eat nine steamed bread so full. Car speeding traffic police are present, then deal with the law. (Writing here, I'm getting the feeling that this sonic argument has a cat cake ...) Take a look at the following analysis, please high play treatise Bar ... After all, you know, as a hooker who hasn't learned the signal system analysis, what does the Fourier change of the classmate, to write, indeed may be biased, toward treatise)

Again, such as the shape of the water waves: first you cast a stone into the water, then the ripple is a situation, after the obvious, you cast a large stone into the water, then on the basis of the large ripples, you can still see the original small ripple. Take the time to hold, you see a node of the level of the high and low, in fact, by the two ripples together to determine the right?

Again, such as sound waves: the study of interference diffraction, the most obvious is that you remember the high school physics often test, small red, in the middle of two broadcasts, some places to listen to the radio is very clear, some local voice is very small. A node sound strength, is composed of two sound waves co-work together to find a point, if it is a crest then this point is a wave of strengthening points, if a crest a trough, then is the sound of the reduction point, hey ~ The question came, two trough what point? Yes, at that time high school always do this topic, is the wave strengthens the point, the answer is wrong to go back to the physics teacher to talk about the heart, I this all nearly 10 years remember. The sound will continue to spread, the waveform continues to advance the point of strengthening the overall strengthening, cutting the total reduction of the place, they will constitute an energy intensity diagram, if you have a God perspective, fantasy has two speakers to broadcast on the playground, to strengthen the imitation of the line to a high point, cut point to a place, from black to white to some color, The strong point is blue and the weakness is black. There is a constant gradient in the middle of the point. is a broadcast example, is the two broadcast example, the question is: Suppose the left waveform constantly pushing to the right, that is, continuous interference, then the right energy distribution map will change?

Pay attention to the problem, is the energy distribution map (energy intensity diagram) Of course, will not change, but the energy will continue to from two holes to the right, push. If you don't understand it, search for the interfering GIF. All the things you see are like this, you see all the moment, but to go through the endless process, such as small a very hard to test to a school, you see only he was admitted, but you do not see the hardship he paid, of course, also may be like Zhengwiro (http://baike.baidu.com/ item/Zhengwiro) That's right ... Regardless, this is not the point, so this is also the old people often say, "3-year-old look at the big 7-year-old look at the old" (now have a scientific basis?) Well, I think if you can analyze it from an empirical point of view, then from a physical point of view it can be explained by Fourier transform: http://baike.baidu.com/link?url=y120_4RlEpMVHDxQ0WPESzOIEPzIne_ MJCCRTUEPIW8UOGKVNQDY0EWXDYHOWWJ3QTJ9SA6OSBY1-MMIFDB5WK)

As you can see, the reaction on the right is the map that carries the energy, and the left side is a reaction.

See again:

Note the quote just quoted: "China has been such a sentence since ancient times:" 3-year-old see big, 7-year-old look at the old ", it simply and clearly summed up the general law of the child's psychological development. From the 3-year-old children's psychological characteristics, personality tendencies, you can see the child's adolescent psychological and personality image of the embryonic stage, and from the 7-year-old child, you can see his middle-aged achievements and exploits. ”

So how much still a little bit of the meaning of the conclusion, well, how to say, see the first to see the document inside there is this sentence, I dare to be at ease here nonsense. Of course, I would like to talk about the verdict if I have a chance later. Ah ~ I think of the Book of Zhouyi ... Forget it too far ... First of all, I want to explain to myself why an image can be decomposed into frequency domain and time domain. From the previous view of the results, the time domain is the image of the present in front of me, what is the frequency domain? What exactly constitutes such a piece of certainty. Oh oh, the time domain is the fruit of that node, the frequency domain is that the component is the cause.

(If you have the opportunity to talk about before the big talk about the pattern of insight and Tsinghua University social Science students a report to illuminate a point of view.) ）

First, remember that the phase is the distance of two peaks.

The next explanation. We have been able to get the frequency domain diagram by the time domain diagram, right ~ ~ ~ can all have to be able!!! Now all we have to do is understand. But I'll give you two sin (x), I say I want an overlay diagram, or energy interference diagram, you should not give me. Why, I didn't tell you how much difference between the two waveforms, if I tell you the difference 0, then the maximum value is able to 2 of the right, if the difference is not 0 plus cycle of the integer times, is not the peak must not reach 2. No, it's not right now, start drawing. I am lazy here, if there is a problem, leave a message. So in order to be able to duplicate the current domain diagram, it takes two graphs, one is the frequency domain diagram and the other is the phase diagram.

(Here it is, not finished,,, but for, the father of China's education has found an argument, in this article, I remember before there is an economic category of related articles is the same for efficient education dissatisfaction ... Okay, so am I. ）

Thoughts on reading Fourier series