How to explain the window function in an easy-to-understand way?
How to explain the window function in an easy-to-understand way?
Why add a window function? –> In order to reduce leakage,
why does leakage occur? —>Because of the non-periodic truncation of the signal, the spectrum is smeared in the entire frequency band. This is a very serious error called a leak.
As shown in the figure below, if the period is truncated, the FFT spectrum is a single spectral line. If it is aperiodic truncation, the spectrum will be tailed, as shown in the middle of the figure, it can be seen that the leakage is very serious. In order to reduce leakage, a window function is applied to the signal (as shown in the red curve in the figure), and the signal obtained after multiplying the original truncated signal by the window function is the signal on the upper right side. It can be seen that at this time, the amplitude of the signal at the start time and the end time is 0, that is to say, within this time length, the signal is a periodic signal, but there is only one cycle. Perform FFT analysis on this signal, and the obtained spectrum is shown below on the right. Compared to the previously unwindowed spectrum, it can be seen that the leakage has improved significantly, but not completely eliminated. Therefore, window functions can only reduce leakage, not eliminate it.
