So for each frequency, we actually need to multiply by a sine wave and a cosine wave and find the amplitudes for each.
因此,对于每个频率,我们实际上需要乘以正弦波和余弦波并找到每个频率的振幅。
Veritasium真理元素
You multiply each point by a sine wave of this frequency and a cosine wave of this frequency and separately add them up.
将每个点乘以该频率的正弦波和该频率的余弦波,然后将它们分别相加。
Veritasium真理元素
Now so far I've only talked about sine waves but if the signal is a cosine wave, then even if you multiply it by a sine wave of the exact same frequency, the area under the curve will be zero.
The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is: