Difference between causality and memorylessness
$begingroup$
I have found the particular definitions.
Causality means that the output of the system does not depend on future inputs, but only on past input.
Memory-less - does not depend on previous values of either input or output.
I am looking for example of systems which are either non-casual or memoryless but not both.
Also i want to check whether I understand it well.
$ T(x[n]) = x[n − n_{0}] $
$T(x[n]) = ax[n] + bx[n − 3]$
Are those an examples of non-casual and memory-less systems?
homework system-identification
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
$endgroup$
add a comment |
$begingroup$
I have found the particular definitions.
Causality means that the output of the system does not depend on future inputs, but only on past input.
Memory-less - does not depend on previous values of either input or output.
I am looking for example of systems which are either non-casual or memoryless but not both.
Also i want to check whether I understand it well.
$ T(x[n]) = x[n − n_{0}] $
$T(x[n]) = ax[n] + bx[n − 3]$
Are those an examples of non-casual and memory-less systems?
homework system-identification
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
$endgroup$
add a comment |
$begingroup$
I have found the particular definitions.
Causality means that the output of the system does not depend on future inputs, but only on past input.
Memory-less - does not depend on previous values of either input or output.
I am looking for example of systems which are either non-casual or memoryless but not both.
Also i want to check whether I understand it well.
$ T(x[n]) = x[n − n_{0}] $
$T(x[n]) = ax[n] + bx[n − 3]$
Are those an examples of non-casual and memory-less systems?
homework system-identification
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
$endgroup$
I have found the particular definitions.
Causality means that the output of the system does not depend on future inputs, but only on past input.
Memory-less - does not depend on previous values of either input or output.
I am looking for example of systems which are either non-casual or memoryless but not both.
Also i want to check whether I understand it well.
$ T(x[n]) = x[n − n_{0}] $
$T(x[n]) = ax[n] + bx[n − 3]$
Are those an examples of non-casual and memory-less systems?
homework system-identification
homework system-identification
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
asked Nov 25 '18 at 17:27
roffensiveroffensive
524
524
add a comment |
add a comment |
2 Answers
2
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$begingroup$
A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values).
The system $$y[n]=x[n]+2x[n+1]$$ is non-causal because it needs to look into the future (by $1$ sample) to compute its output. The system $$y[n]=3big(x[n]big)^2$$ is memoryless (and necessarily causal) because it only needs the current input sample $x[n]$ to compute the output.
The systems in your question are both causal and have memory (if $n_0>0$).
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
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add a comment |
$begingroup$
Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values.
The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition to current input sample).
Also note that a noncausal system cannot be memorlyess is it must depend on future values (and hence exhibit memory) to be noncausal.
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
$endgroup$
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
add a comment |
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2 Answers
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active
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2 Answers
2
active
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$begingroup$
A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values).
The system $$y[n]=x[n]+2x[n+1]$$ is non-causal because it needs to look into the future (by $1$ sample) to compute its output. The system $$y[n]=3big(x[n]big)^2$$ is memoryless (and necessarily causal) because it only needs the current input sample $x[n]$ to compute the output.
The systems in your question are both causal and have memory (if $n_0>0$).
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
$endgroup$
add a comment |
$begingroup$
A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values).
The system $$y[n]=x[n]+2x[n+1]$$ is non-causal because it needs to look into the future (by $1$ sample) to compute its output. The system $$y[n]=3big(x[n]big)^2$$ is memoryless (and necessarily causal) because it only needs the current input sample $x[n]$ to compute the output.
The systems in your question are both causal and have memory (if $n_0>0$).
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
$endgroup$
add a comment |
$begingroup$
A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values).
The system $$y[n]=x[n]+2x[n+1]$$ is non-causal because it needs to look into the future (by $1$ sample) to compute its output. The system $$y[n]=3big(x[n]big)^2$$ is memoryless (and necessarily causal) because it only needs the current input sample $x[n]$ to compute the output.
The systems in your question are both causal and have memory (if $n_0>0$).
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
$endgroup$
A causal system does not need to know the future in order to compute its output. A memoryless system computes the output only from the current input. A memoryless system is always causal (as it doesn't depend on future input values), but a causal system doesn't need to be memoryless (because it may depend on past input or output values).
The system $$y[n]=x[n]+2x[n+1]$$ is non-causal because it needs to look into the future (by $1$ sample) to compute its output. The system $$y[n]=3big(x[n]big)^2$$ is memoryless (and necessarily causal) because it only needs the current input sample $x[n]$ to compute the output.
The systems in your question are both causal and have memory (if $n_0>0$).
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
edited Nov 26 '18 at 9:19
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
answered Nov 25 '18 at 18:02
Matt L.Matt L.
50.9k23889
50.9k23889
add a comment |
add a comment |
$begingroup$
Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values.
The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition to current input sample).
Also note that a noncausal system cannot be memorlyess is it must depend on future values (and hence exhibit memory) to be noncausal.
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
$endgroup$
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
add a comment |
$begingroup$
Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values.
The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition to current input sample).
Also note that a noncausal system cannot be memorlyess is it must depend on future values (and hence exhibit memory) to be noncausal.
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
$endgroup$
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
add a comment |
$begingroup$
Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values.
The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition to current input sample).
Also note that a noncausal system cannot be memorlyess is it must depend on future values (and hence exhibit memory) to be noncausal.
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
$endgroup$
Output of a memoryless system depends only on the current input value and therefore every memoryless system is also causal; since a causal system's output cannot depend on the future input values.
The converse in general is not true; causal systems can be memoryless as well as can exhibit memory (if their outputs depend on the past input values in addition to current input sample).
Also note that a noncausal system cannot be memorlyess is it must depend on future values (and hence exhibit memory) to be noncausal.
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
answered Nov 25 '18 at 18:06
Fat32Fat32
15.6k31232
15.6k31232
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
add a comment |
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
The OP's definition of a memoryless system requires that outputs not depend upon past inputs or outputs, but says nothing about whether they may rely upon future outputs. I would think that time-reversing a system that neither causal nor memoryless would yield a system that is both.
$endgroup$
– supercat
Nov 25 '18 at 23:09
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
@supercat OP's definition of memoryless system is (then) incomplete... anyway I've put my answer wrt. to the correct definition.
$endgroup$
– Fat32
Nov 25 '18 at 23:26
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
$begingroup$
It might be good to mention that your use of "memoryless" differs from that of the OP.
$endgroup$
– supercat
Nov 26 '18 at 1:31
add a comment |
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