傅立葉變換，將時域信號轉為頻域信號

傅立葉變換，就把在時間上的信號變成在頻域上的信號  Fourier transform, the signal in time is turned into a signal in the frequency domain


Apr 20, 2016 at 10:13 PM

今天講一點有關我自己專業的事情. 你們有沒有聽說過傅立葉變換？你們知道傅立葉變換是做什麼用處的嗎？ 比如說你彈吉他，每一根弦, 手按的每一個位置都是一個key, 比如G, 或者C. 你可以把這個音唱出來. 唱出來就是聲波, 聲波是波, 如果用信號來描述的話, 就是在時間x軸上, 在音量Y軸上展開的一個正弦曲線.

Dear Xi and Wang, Jackie is complaining again. Have you asked her if she wants Cheetos? Every time you play with Cheetos, someone will suffer, what happened this time? Although I was inexplicably brought here from the beginning, there have been people harassing me from time to time, but recently I have not seen it so much. I saw you in the South China Sea, South Korea, the Philippines, Japan and the United States. I understand it little by little. Behind me, the vast forces of power, may be related to the US military? Is that true? From the beginning, was it them find trouble with me? Or is that the shadow of the US government? But why are you coming in this group? Is it a partnership or a Cheetos relationship? I am a fool! You are not telling me the truth!  Tell you a little about my own profession today. Have you heard of the Fourier transform? Do you know what the Fourier transform is for? For example, if you play the guitar, every string, every position of the finger is a key, such as G, or C. You can sing this key. Singing is sound waves, sound waves are waves, if you use signals to describe this case, it is a sinusoid that is spreading on the volume Y axis on the time x axis.

http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/

https://www.google.com/search?q=white+noise+frequency&biw=320&bih=460&prmd=visn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi_utqs-p7MAhVLwWMKHRxrAMUQ_AUIBygC#imgrc=qQ0JqJ-rgEC-TM%3A

如果把這個信號進行傅立葉變換，就把在時間上的信號變成在頻域上的信號，在吉他上那個音，或者是在鍵盤上的那個音，不管哪一個樂器上的音，只要是同一個音，它的頻率就是一定的. 當信號被傅立葉變換后，就是在X軸頻域的特定頻率上, 有一條豎線，也就是在時域上的一個正弦線波，對應在頻域上是一條在特定頻率的豎線！明白了嗎？ 當我們去海邊的時候, 我們會聽見 「花...........」 的海浪聲, 這個海浪聲象 在撫摸我們的心靈的各個角落，五臟六腑都徹徹底底地舒坦，而這種「花...........」的聲音，在數學上我們稱之為白雜訊，white noise , 因為在頻域的表示中，從低頻到高頻，是一條橫線，也就是說海浪包括了所有的頻率. 而有意思的是，白雜訊在時域的圖也是一條橫線，反正白雜訊把所有的信號所有的頻率都包括在裡邊了！音樂是有曲調的，曲調就是頻率的變化，人在心理上對頻率的變化, 是有情感反應的. 而沒有頻率變化的白雜訊，刺激了人的聽覺的所有頻率，當在適當的響度，就像對你的耳朵進行心理上的按摩，所以很舒服的. 幻想著有一天可以聽你彈吉他，或者一起去海邊聽海浪！

If this signal is Fourier transformed, the signal in time is changed to the signal in the frequency domain. The sound on the guitar, or the sound on the keyboard, no matter which instrument  the sound is on, as long as it is the same sound whose frequency is constant. When the signal is Fourier transformed, it is a vertical line at a specific frequency in the X-axis frequency domain, that is, a sinusoidal wave in the time domain, corresponding to the frequency domain is a vertical line at a specific frequency! do you understand? When we go to the beach, we will hear the sound of the waves of "huuuuuaaaa.....". This sound of the waves is touching every corner of our hearts, and the internal organs are completely comfortable. And the sound of this "huuuuuaaaa....." is mathematically called white noise, white noise, because in the frequency domain representation, from low frequency to high frequency, it is a horizontal  line. That is to say the wave includes all the frequencies. What's interesting is that the white noise in the time domain is also a horizontal line. Anyway, the white noise includes all the frequencies of all the signals in it! Music is tune, tunes are changes in frequency, and people are emotionally responsive to changes in frequency. White noise with no frequency changes, stimulates all frequencies of human hearing, when in appropriate volume, It's like a psychological massage to your ears, so it's very comfortable. I dream that one day I can listen to you playing guitar, or go to the beach to listen to the waves!