Are Instantaneous and Causal Systems the Same Concept?

[Shackman]

Just a quick concept check. It seems to me that all instantaneous (memoryless) systems are causal because the output of a memoryless system at an instant t depends solely on the input at an instant t, and causal systems are systems whose output depends on past and present inputs only. Is this correct or are my ideas of memoryless and causal systems incorrect?

 

[Bob S]

You might want to add the concept of such theorems as the real-part (or imaginary-part) sufficiency theorem, in essence stating that the real and imaginary parts (like in electrical circuits) are related by the Kramers-Kronig causality (dispersion) equations. Knowing either the real (or imaginary) impedance of a circuit at all frequencies completely determines the other.

 

[Mr.Green]

I think there are some confusion in the concept of a Causal system and a Memoryless system... the two are basically different.

A system is called Causal if its output y(t) at an arbitrary time t = to depends on only the input x(t) for t =< to. That is, the output of a Causal system at the present time depends only on the present and/or past values of the input, not on its future values. (Hwei P. Hsu, Signals and Systems, Schaum's Outlines)

The memoryless is different... its output depends on the present input not on the present and/or past values.