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Application: distinguish a small signal that is near a large signal - high dynamic range windows

Let's say that you have two tones, that are close, but far enough apart that their main lobe do not overlap. However, one signal is very large and the other is small. What you care about is that all of the side lobes have as much attentuation as possible, so that the leakage from the big signal does not overwhelm the small signal. This is opposite to a high resolution window and is called a high dynamic range window.

An example is shown in figure 19. In this example we have a 1 Hz bin width, a signal with amplitude 1 at 5.5 Hz, and a signal with amplitude 0.0015 at 13.5 Hz (i.e. 8 bins away). The rectangular window is really bad here. We cannot even see the small 13.5 Hz at all. The Kaiser is better. We can at least see that something is going on at 13.5, although we don't the true picture. The Hann window is the best, we can see the 13.5 Hz as a distinct peak with correct amplitude. Compare this back to figure 18 and look at amplitude at 8.5 bins. The attentuation of the Hann window is just below 0.001, whereas the attentuation of Kaiser is well above it.

Figure 19: Comparison of two signals that have very different amplitudes with different windows

Image window_comparison_dyn_rang


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