Phase shifter vs simple delay3/2/2023 ![]() You would know when the light source was turned on and off and may have an almost instant optical system response time, but the time you need to sample the returned signal would be subject to your delays. One example might be measuring the response of a system with a modulated light source. If your sample time was based on some signal you generated and you expecting to be sample a signal response then again you need to take into account the delay. However, if you were sampling a signal that was changing and were relying on knowing the time of your sample then you need to know that the signal you are sampling has been delayed, in this case by 416us. A signal well below the cut-off frequency will simply be delayed by 416us but otherwise be fine, as illustrated below for a 500Hz sine wave. So, why should you care about this delay or phase shift? Well, if you are monitoring a constant sine wave then it probably won’t matter much. That is to be expected – if you double the frequency the phase shift doubles. If you double the frequency you would double the phase shift from a fixed time delay. Now you can see that in the area of constant group delay the phase actually changes linearly with frequency as would be expected. Changing the x-axis to a linear scale makes it clearer. ![]() A group delay can be considered as a varying phase shift so plotting that results in:Īs this is on a log-lin scale it is not obvious what is happening. So, even well below the cut-off frequency there is an almost constant group delay of around 416us. With a 1kHz bandwidth you will see a group delay response below. Take a simple 4 pole Butterworth filter as an example. The time you sample the signal will not necessarily be the time of the actual event before signal processing. One way in which it might affect you is if you are sampling a signal. It may not matter that it is there, but you need to be aware just in case. Where $\phi$ is phase difference from input to output.You may or may not have thought about group delays in your electronics signal processing chain, but it is almost certainly there. If you measure this signal at the transmission line end, $y(t)$, it might come somewhere like this: 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.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |