Mixing
Shannon Entropy of a periodic signal
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We have a source $X$ with alphabet size equal to $N$. The Shannon entropy is defined as
$$E(X)=-sum _{i=1}^{N}p_{i}cdotlog _{2}p_{i}$$
where $p_i$ is the probability of symbol $i$ appearing in the stream of characters of the message.
If the source transmits $M>N$ symbols so that the resulting signal is periodic (i.e. it "completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods", from Wikibooks) what is the entropy worth in this case?
information-theory entropy
asked Jan 29 at 14:15
MarkMark
3,46451947
$endgroup$
add a comment |
$begingroup$
We have a source $X$ with alphabet size equal to $N$. The Shannon entropy is defined as
$$E(X)=-sum _{i=1}^{N}p_{i}cdotlog _{2}p_{i}$$
where $p_i$ is the probability of symbol $i$ appearing in the stream of characters of the message.
If the source transmits $M>N$ symbols so that the resulting signal is periodic (i.e. it "completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods", from Wikibooks) what is the entropy worth in this case?
information-theory entropy
asked Jan 29 at 14:15
MarkMark
3,46451947
$endgroup$
$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16
add a comment |
$begingroup$
We have a source $X$ with alphabet size equal to $N$. The Shannon entropy is defined as
$$E(X)=-sum _{i=1}^{N}p_{i}cdotlog _{2}p_{i}$$
where $p_i$ is the probability of symbol $i$ appearing in the stream of characters of the message.
If the source transmits $M>N$ symbols so that the resulting signal is periodic (i.e. it "completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods", from Wikibooks) what is the entropy worth in this case?
information-theory entropy
asked Jan 29 at 14:15
MarkMark
3,46451947
$endgroup$
We have a source $X$ with alphabet size equal to $N$. The Shannon entropy is defined as
$$E(X)=-sum _{i=1}^{N}p_{i}cdotlog _{2}p_{i}$$
where $p_i$ is the probability of symbol $i$ appearing in the stream of characters of the message.
If the source transmits $M>N$ symbols so that the resulting signal is periodic (i.e. it "completes a pattern within a measurable time frame, called a period and repeats that pattern over identical subsequent periods", from Wikibooks) what is the entropy worth in this case?
information-theory entropy
information-theory entropy
asked Jan 29 at 14:15
MarkMark
3,46451947
asked Jan 29 at 14:15
MarkMark
3,46451947
edited Jan 29 at 16:44
Mark
asked Jan 29 at 14:15
MarkMark
3,46451947
asked Jan 29 at 14:15
MarkMark
3,46451947
asked Jan 29 at 14:15
MarkMark
3,46451947
3,46451947
$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16
add a comment |
$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16
$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16
add a comment |
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$begingroup$
$N$ is the alphabet size (how many available symbols there are to choose from at each time), or is the block length (related to the period?)
$endgroup$
– leonbloy
Jan 29 at 15:31
$begingroup$
@leonbloy thanks, I edited my post
$endgroup$
– Mark
Jan 29 at 16:46
$begingroup$
It should be $H(X)$ instead of $E(X)$. Also, I don't understand what relevance has $M>N$, and what relation (if any) has $M$ with the period.
$endgroup$
– leonbloy
Jan 29 at 18:16