Confusion understanding causality?

Question

I already know the simple definition that causal system is the one that does not depend on future values of input but today i was confused as i came across a new definition of causality after reading "signal processing first "about causality as shown in attached snapshots

I have attached two pages snapshots and i have drawn a thin red line to left side of common para, para that occurs in both snapshots

As shown in common para in second line ,"cause does not precede corresponding effect"

This statement is about causal filter but what does this statement means in simple words?

Both snapshots contain a table ,upward snapshot contains table of non causal filter

Bottom snapshot contains table of causal filter

We can see from table of causal filter that both input and start at same value of time (n=0)while table of non_causal filter shows that output starts at earlier value of time(n=-2) while input starts at a later value of time(n=0),thus Indicating that output(effect)precede input(cause) in case of non-causal filter

Answer 1

If you break down the sentence it is saying that a causal system is one where the input does not precede (come before in time) the output. That is just wrong. The definition of a causal system, using the impulse response, is that: $h[n]=0, \text{ for all } n<0$. This says that when the input is an impulse at $n=0$, the output should be zero until and including time index $n-1$. Once $n=0$ happens, the output can go non-zero. Put into words, this says that the output does not precede the input. This property of causal systems can be remembered by thinking $\text{causal} \approx \text{cause and effect}$.

I think you'd be surprised how many typos and errors there are in textbooks and even some research articles. You can see how swapping the words input and output would be a likely mistake when writing an entire book. Textbooks even anticipate this and often will release something called an errata which is a document laying out the errors and fixes that have been brought to their attention.

Answer 2

The statement is not correct. In a causal system, the cause (i.e. input) does indeed precede (come before in time) the corresponding effect (output).

The correct statement is the cause doesn't follow the corresponding effect.

"Cause creates the effect", so in a causal system, Cause ($x[n]$) will always come first and then the corresponding effect ($y[n]$).

A causal $h[n]$ can not use samples $x[n+1], x[n+2], x[n+3], ...etc$ in order to create $y[n]$. $h[n]$ can only use $x[n], x[n-1], x[n-2],...etc$.