Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
Q1: The mathematical definition of causality states that a system is causal if all output values, y[n0] , depend only on input values x[n] for n<=n0. Another way of saying this is the present output depends only on past and present input values. Then, it says that y[n]=x[n]+x[n-1]+y[n+1] is a non-causal system and also note that y[n+1] can be written in terms of x[n]. How can we write y[n+1] in terms of x[n]? I know it's a very basic questions but... sorry!
Q1 EDIT: I'll make it simpler than what I said before. You can use y[n+1]=x[n+1]+x[n]+y[n+2]. Then you can see that y[n+2] can be expressed with other samples of x[n] and y[n]. This leads to an infinite summation,
hence, [LATEX]y[n+1]=\sum^{\infty}_{k=n} x[k]+x[k+1]\ \ ,[/LATEX]
Q2 It's just terminology, so don't let it confuse you. If someone called them "Jim" and "Sally", would you worry that they are human? No, they are just labels. However, I believe that the origin of the labels comes from the fact that impulse responses of a causal system look like one type and impulse responses of a noncausal system look like the other type. So, the naming has a logical basis. So, your question should really be, "what is the origin of the terminology?". Hopefully, my answer about that is correct, or "correct enough".
The mathematical definition of causality states that a system is causal if all output values, y[n0] , depend only on input values x[n] for n<=n0. Another way of saying this is the present output depends only on past and present input values. I'm still confused.
Note that it talks about inputs. When you throw outputs into equation, it no longer applies. Hence the confusion in my examples. I thought you would catch me.
I don't get the summation expression. You had y[n+1]=x[n+1]+x[n]+y[n+2] but "y[n+2]" is nowhere in the summation. I'm sorry if I'm sounding just plain dumb.
But the terms "causal" and "non-causal" have specific meanings in the given context. So, there should be reason for calling them so. Yes, my question should have been about the origin of terminology. I was confused because I didn't see any reason for calling a right-sided sequence 'causal' and the left-sided sequence 'non-causal'. I don't see any role of the following definition in their description or labeling: The mathematical definition of causality states that a system is causal if all output values, y[n0] , depend only on input values x[n] for n<=n0. Another way of saying this is the present output depends only on past and present input values. I'm still confused. Thanks.
I'm confused on whether you are satisfied with my answer above. Is my explanation that the terminology comes from the signals being compared to impulse responses for causal and anti-causal systems sufficient?
OK, let me clarify what I was trying to say. It turns out that a causal system has an impulse response that is a right sided signal. It also happens that an anti-causal system has an impulse response that is a left sided signal. So, the systems are the things that can be causal, anti-causal or non-causal. The signals are not really best described that way, but somehow the terminology has been carried over.I believe I should just understand that a right-sided sequence is called 'causal' and the left-sided sequence 'non-causal'.
OK, let me clarify what I was trying to say. It turns out that a causal system has an impulse response that is a right sided signal. It also happens that an anti-causal system has an impulse response that is a left sided signal. So, the systems are the things that can be causal, anti-causal or non-causal. The signals are not really best described that way, but somehow the terminology has been carried over.
Also, note that there is a difference between "anti-causal" and non-causal. An anti-causal system is analogous to the causal system in that it does not depend on past value. However, a non-causal system is just one that is not causal, which is not necessarily the same thing.