# Confusion understanding causality?

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  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.

• Will you please kindly elaborate. What do you mean by "causal=cause and effect " ??
– Man
Apr 11 '20 at 13:29
• That is just how I would remember it. There is a cause (input) and then an effect (output). Just a simple way to boil it all down, its like you trip on a rock and then you fall, you turn on the stove top and then the water in the pot starts to boil. You don't fall before you trip and your water doesn't boil before you turn on the stove: Cause and effect Apr 11 '20 at 13:37
• And what about non causal filters? Can and does, their output precede their input?
– Man
Apr 11 '20 at 14:20
• Non-causal means that the output can precede the input. There is also anti-causal, which means the output always precedes the input. Apr 11 '20 at 14:38

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 $$x[n], x[n-1], x[n-2],...etc$$.

• Yup. I think it's just a typo. Apr 10 '20 at 19:48
• If it is typo then why this typo occurs in multiple and even in latest edition of book.
– Man
Apr 11 '20 at 9:54
• @man can't comment on why the typo keeps occuring, but conceptually it is incorrect Apr 11 '20 at 9:57
• Please kindly check the updated question contents, that may gives you more idea
– Man
Apr 11 '20 at 11:24