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Modified grammar and word usage for clarity.
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lennon310
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Confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system depends neither on past (for the causal case) nor on future values of the input but on current ones to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to have a constant delay, i.e., to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ with a fixed integer $k$. So, in general, a memory-less system can have the following form, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, which that cannot look ahead in the future, only $k \ge 0$ are allowed.

Confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system depends neither on past (for the causal case) nor on future values of the input but on current ones to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to have a constant delay, i.e., to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ with a fixed integer $k$. So, in general, a memory-less system can have the following form, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, which cannot look ahead in the future, only $k \ge 0$ are allowed.

Confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system depends neither on past (for the causal case) nor on future values of the input but on current ones to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to have a constant delay, i.e., to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ with a fixed integer $k$. So, in general, a memory-less system can have the following form, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems that cannot look ahead in the future, only $k \ge 0$ are allowed.

A confusionConfusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negativenegative time indices".

A strict memory-less system does dependdepends neither on past (for the causal case) nor on future values, only of the input but on current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to allowhave a constant delay, i.e., to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ ofwith a fixed integer $k$: So. So, globallyin general, a memory-less system can affordhave the following shapeform, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, thatwhich cannot look ahead in the future, only $k\ge 0 $$k \ge 0$ are allowed.

A confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system does depend neither on past (for the causal case) nor on future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$: So, globally, memory-less system can afford the following shape, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, that cannot look ahead in the future, only $k\ge 0 $ are allowed.

Confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system depends neither on past (for the causal case) nor on future values of the input but on current ones to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to have a constant delay, i.e., to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ with a fixed integer $k$. So, in general, a memory-less system can have the following form, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, which cannot look ahead in the future, only $k \ge 0$ are allowed.

edited body
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Laurent Duval
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A confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system does depend neither on past (for the causal case) nor on future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$: So, globally, memory-less system can afford the following shape, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, that cannot look ahead in the future, on:yonly $k\ge 0 $ are allowed.

A confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system does depend neither on past (for the causal case) nor on future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$: So, globally, memory-less system can afford the following shape, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, that cannot look ahead in the future, on:y $k\ge 0 $ are allowed.

A confusion may arise, for causal systems, from mistaking "having negative signal values (amplitudes)" and "depending on negative time indices".

A strict memory-less system does depend neither on past (for the causal case) nor on future values, only the current ones, to determine the current value of the output. The output at $n$ only depends on inputs at $n$. For a strict memory-less and causal system, you could not depend on former (negative, in a way relative to the current index) time indices.

By extension, some allow memory-less systems to allow a constant delay, i.e. to hold only one value at a given lag: the output at $n$ only depends on inputs at $n-k$ of a fixed integer $k$: So, globally, memory-less system can afford the following shape, with $k$ any integer:

$$y[n] = f(x[n-k])\,.$$

For realizable causal systems, that cannot look ahead in the future, only $k\ge 0 $ are allowed.

neither... nor
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Laurent Duval
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Laurent Duval
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Laurent Duval
  • 32.3k
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  • 105
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added details
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Laurent Duval
  • 32.3k
  • 3
  • 35
  • 105
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Source Link
Laurent Duval
  • 32.3k
  • 3
  • 35
  • 105
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