Where $\phi$ is phase difference from input to output. The thread remains idle for the duration of that delay. If you measure this signal at the transmission line end, $y(t)$, it might come somewhere like this: You need to understand that a delay introduced by time.sleep () is rather a lack of instruction. Take long transmission line with simple quasi-sinusoidal signal with an amplitude envelope, $a(t)$, at its input Here's a really interesting article about this: įor those who still cannot chalk the difference here is an simple example If a spike were inserted in the middle of the signal, the filter would not anticipate that. It's definitely weird, but a way to think about it is that since the envelope has a very predictable shape, the filter already has enough information to anticipate what is going to happen. It seems like a paradox, since it would appear that the filter has to "see" into the future. The crazy thing? Causal filters can have negative group delay! Take your gaussian multiplied by a sinusoid: you can build an analog circuit such that when you send that signal through, the envelope's peak will appear in the output before the input. So, in a way, the group delay is giving you information about how the sidebands will be delayed relative to that carrier frequency, and applying that delay will change the shape of the amplitude envelope in some way. The amplitude modulation will take the sinusoid's peak, and introduce sidebands at neighboring frequencies. Now, remember how we're using an amplitude-modulated sinusoid. In other words, at some frequency, the group delay is telling you approximately how the phase response of the neighboring frequencies relate to the phase response at that point. The derivative gives you a linearization of the phase response at that point. I like to think about this by going back to the definition of group delay: it's the derivative of phase. This envelope has a shape to it, and in particular, it has a peak that represents the center of that "packet." Group delay tells you how much that amplitude envelope will be delayed, in particular, how much the peak of that packet will move by. Picture a short sine wave with an amplitude envelope applied to it so that it fades in and fades out, say, a gaussian multiplied by a sinusoid. ![]() Group delay is a little more complicated. They don't both measure how much a sinusoid is delayed.
0 Comments
Leave a Reply. |