# Shannon Entropy of a periodic signal

We have a source $$X$$ with alphabet size equal to $$N$$. The Shannon entropy is defined as $$E(X)=-\sum _{i=1}^{N}p_{i}\cdot\log _{2}p_{i}$$ 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?

• $N$ 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?) – leonbloy Jan 29 at 15:31
• @leonbloy thanks, I edited my post – Mark Jan 29 at 16:46
• 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. – leonbloy Jan 29 at 18:16