blackcat1402

windowing_ta

All Signals Are the Sum of Sines. When looking at real-world signals, you usually view them as a price changing over time. This is referred to as the time domain. Fourier’s theorem states that any waveform in the time domain can be represented by the weighted sum of sines and cosines. For example, take two sine waves, where one is three times as fast as the other–or the frequency is 1/3 the first signal. When you add them, you can see you get a different signal.


Although performing an FFT on a signal can provide great insight, it is important to know the limitations of the FFT and how to improve the signal clarity using windowing. When you use the FFT to measure the frequency component of a signal, you are basing the analysis on a finite set of data. The actual FFT transform assumes that it is a finite data set, a continuous spectrum that is one period of a periodic signal. For the FFT , both the time domain and the frequency domain are circular topologies, so the two endpoints of the time waveform are interpreted as though they were connected together. When the measured signal is periodic and an integer number of periods fill the acquisition time interval, the FFT turns out fine as it matches this assumption. However, many times, the measured signal isn’t an integer number of periods. Therefore, the finiteness of the measured signal may result in a truncated waveform with different characteristics from the original continuous-time signal, and the finiteness can introduce sharp transition changes into the measured signal. The sharp transitions are discontinuities.

When the number of periods in the acquisition is not an integer, the endpoints are discontinuous. These artificial discontinuities show up in the FFT as high-frequency components not present in the original signal. These frequencies can be much higher than the Nyquist frequency and are aliased between 0 and half of your sampling rate. The spectrum you get by using a FFT , therefore, is not the actual spectrum of the original signal, but a smeared version. It appears as if energy at one frequency leaks into other frequencies. This phenomenon is known as spectral leakage, which causes the fine spectral lines to spread into wider signals.


You can minimize the effects of performing an FFT over a noninteger number of cycles by using a technique called windowing. Windowing reduces the amplitude of the discontinuities at the boundaries of each finite sequence acquired by the digitizer. Windowing consists of multiplying the time record by a finite-length window with an amplitude that varies smoothly and gradually toward zero at the edges. This makes the endpoints of the waveform meet and, therefore, results in a continuous waveform without sharp transitions. This technique is also referred to as applying a window.

Here is a windowing_ta library with J.F Ehlers Windowing functions proposed on Sep, 2021.

Library "windowing_ta"

hann()

hamm()

fir_sma()

fir_triangle()

Donate TRC20 USDT to below address, 5USDT per monthly sub, 50USDT per yearly sub: TNz84MjJTWUUUyQFpPNjaAU7J2SwhJJ7j9
Note: USDT_TRC20 deposits sent from decentralized exchanges are not yet supported.
Pine脚本库

本着真正的TradingView精神,作者将此Pine代码以开源脚本库发布,以便我们社区的其他Pine程序员可以重用它。向作者致敬!您可以私下或在其他开源出版物中使用此库,但在出版物中重用此代码受网站规则约束。

免责声明

这些信息和出版物并不意味着也不构成TradingView提供或认可的金融、投资、交易或其他类型的意见或建议。请在使用条款阅读更多信息。

想使用这个脚本库吗?

复制以下行并将其粘贴到您的脚本中。