傅立葉變換

傅里葉變換 Fourier transform

昨天講到了數字鋼琴有那麼清亮的音色。一般的模擬信號，比如說一個正弦波，如果不告訴我，那我用什麼辦法知道它的頻率呢？在數學上，那就是用不同的頻率信號跟它相乘，只有跟它頻率一樣的乘出來的能量最大，別的頻率所乘結果都是零。所以才有了這個數學表示e^jθ= cosθ+j sinθ, θ = ωt, ω可以是任何頻率，t是時間，θ就是相位角度。所以單個正弦波在頻域的表示，就是在那個頻率上有一個表示能量的垂直線。所以才會有富里葉變換，把時域信號變成頻域信號.

https://youtu.be/Ohp6Okk_tww

I talked about the digital piano yesterday. It has such a clear tone. A normal analog signal, like a sine wave, If you don't tell me, how do I know its frequency? Mathematically, that means To multiply the signal with different frequencies. multiplying it with the same frequency as it produces the most energy, and multiplying it with at any other frequency will get zero. That's why we have the mathematical expression e ^ j θ = cos θ + j sin θ, θ = ω t, ω can be any frequency, t is time, θ is phase angle. So the representation of a single sine wave in the frequency domain is a vertical line of energy at that frequency.  Hence the Fourier transform, which converts time-domain signals into frequency-domain signals.