A causal system is one where the output at any time depends only on the present and past values of the input, not future values. This means that the system does not “anticipate” future inputs.
Present and past effects, future doesnt effect → casual
- All real-time physical systems are causal. Since time only moves forward, effect always follows cause in physical systems.
- All memoryless systems are causal. A memoryless system is one where the output depends only on the current input value, meaning it does not rely on past or future inputs.
Maybe the independent variable is not time. Then, causality is not an essential constraint.
- In image processing, we can move both left and right, up and down.
y[n]=x[n]−x[n+1], y(t)=x(t+1): Non causal (not )
y[n]=x[−n] ? Is fine in terms of causality if n > 0. But if n<0, then it behaves by the future inputs. Than this system is not causal.
y(t)=x(t)cos(t+1)? The cosine function cos(t+1) is simply a time-varying multiplier and does not introduce dependency on future values of x(t). The system is causal and memoryless.