Shannon's uncertainty question

[Calmstorm]

Homework Statement

:

If I were to use a two-tone image e.g. fax, and were to transmit it line-by-line, where the the individual pixels which make up the line were independent of each other, how would I measure the uncertainty at the transmitter? Also what would the length of the the transmited sequence be if the image was a square NxN image?


2. The attempt at a solution

I think the uncertainty is H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}
where:
W=number of white pixels in the sequence
Pi=probability of a white pixel.
B=number of black pixels in seqence
Qj=probability of a black pixel.

Any ideas would be very helpful...thank you in advance!

 

[EnumaElish]

Please do not cross-post.

 

[piercas]

I can confirm that your calculation for uncertainty is correct. The Shannon's uncertainty question deals with the concept of information theory, which is used to measure the amount of uncertainty or randomness in a system. In this case, the system is a two-tone image being transmitted line-by-line. Your equation takes into account the number of white and black pixels, as well as their respective probabilities, to calculate the overall uncertainty in the transmission.

To answer your second question, the length of the transmitted sequence for a square NxN image would be N^2, as there would be N lines with N pixels in each line. This is because each pixel is being transmitted independently, so the total length would be the product of the number of lines and the number of pixels in each line.

I hope this helps clarify the concept of Shannon's uncertainty and how it applies to your specific question. Keep up the good work in exploring and understanding information theory!