What is a non causal system and its function?

what is a non causal system ? can such a system exist in real ? if it exists for what purpose is it used? please explain to me in detail........

thanks....

Re: NON CAUSAL SYSTEM

Non-causal means that the response of the system needs to start before the excitation. For example, if you add an impulse to the input at a certain time T, a normal (causal) system will start responding from time T, T+1, ...
A non-causal system would start its response before the input, e.g. T-10, T-9, ... T, T+1, ...
This is of course not a natural system because it would need to predict the future and start responding before the input.

Nevertheless it might be possible to make such a system, by:
- delaying the input by a certain time but also making a non-delayed copy of the input available. Thanks to the early copy of the input the system can start responding before the delayed input.
- replacing the time dimension T by the space dimension, such as in 2D image processing (pixel X,Y) . The "previous" pixels (X-10, Y-...) are known because an entire image is processed after it has come in.

Out of curiosity, this question reeks of a homework assignment. Why do you ask it?

Re: NON CAUSAL SYSTEM

first thanks for replying me MR . vomit.

and i actually asked this question because, i was not satisfied with my prof. explanation on this topic..... and i have one more doubt.....

you said a causal system will react after applying an input and a non causal will rely on future ones...... if it is so..... then can we treat this system as a virtual one? because how can a system respond or give any o/p without giving any real input? if the input is virtual and so is the o/p..... then is the whole system virtual ... does it have any use in the real world use?

Re: NON CAUSAL SYSTEM

You're right to say that a non-causal system is not really a system we encounter in nature, and therefore "virtual".
In nature, system responses follow the cause=excitation (so they are called causal).

To give an example of a non-causal system: suppose we want to make a perfect low-pass filter with a cutoff frequency. Everything before that frequency is passed (filter multiplies by 1) and everything after that frequency is multiplied by zero.

Look at **broken link removed** page 22.
The frequency response is the red line. I think there is an error, and the line must be between 1.0 (high) and 0.0 (low), not -0.5.

You see that the sin(x)/x impulse response (right diagram) would need to start before time 0!
In real life this is not possible (so there are no such filters with resistors/capacitors etc, and there are approximations like Butterworth and Chebychev that try to approach the ideal filter while optimizing some tradeoff factor, like ripple or steepness)

In digital filtering, where a computer can access previous and following samples, this is possible! The response will of course take some extra delay to come out (we can't predict te future).
The sampling stage can have some memory built-in, and delay the input by a finite number of samples (e.g. 50 in the figure from the PDF) and therefore have the value of sample T-50 available when calculating the output for T=0.

So at the calculation for the output centered on T=0, we are actually at T=+50 of the real signal that is being sampled. But because the sampling stage has a delay of 50 samples, it seems that we have access to all samples going from T=50 (100 samples ago), to T=0 (50 samples ago), and T=-50 (50 samples in the future, that's the sample coming in right now thanks to our calculation delay).

The output will have a real time delay of 50 samples (output T=0 is produced at real time T=50), but for some applications a fixed latency is not a problem.

Re: NON CAUSAL SYSTEM

thanks vomit....... i understood it now!!!

NON CAUSAL SYSTEM

such system doesn't exisit in real world,if i define noncausal system,these are the system in which output depends upon future time,like y(t)= x(t+1)

Re: NON CAUSAL SYSTEM

In DSP non causal system are those that use feature input or feature output for computing current input.
In reality non causal system dont exist and hence they could not be implemented.

Example of non causal system, with x=input, y=output

1) y = x(n+1) + x(n+2) + y(n+1)

Re: NON CAUSAL SYSTEM

Mr. Vomit,

You mentioned something about replacing T from time dimension to space dimension, and use in 2-D image processing. could you explain more about it, and if you have any sources so I can study more about it, please tell me. thanks