Shannons :calculating simple uncertainty

  • Thread starter Calmstorm
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In summary, the speaker is asking how to measure uncertainty at the transmitter if a two-tone image is transmitted line-by-line with independent pixels. They also inquire about the length of the transmitted sequence for a square NxN image. The suggested formula for measuring uncertainty is H(X)= - W{ Pilog(Pi) } -B{Qj log (Qj)}, where W represents the number of white pixels, Pi is the probability of a white pixel, B represents the number of black pixels, and Qj is the probability of a black pixel. The speaker requests any helpful ideas.
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Calmstorm
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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?

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!
 
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It's great that you're looking into calculating the uncertainty in your transmission of a two-tone image. Shannon's theory of communication is a fundamental concept in information theory and it can definitely be applied in this scenario.

To measure the uncertainty at the transmitter, you can use the formula H(X) = -∑P(x)logP(x), where P(x) is the probability of a particular pixel value (white or black) in the sequence. This formula takes into account the different probabilities of each pixel value and calculates the overall uncertainty of the sequence.

In your case, for a two-tone image, there are only two possible pixel values (white or black) and their probabilities can be calculated based on the number of white and black pixels in the sequence. So, the length of the transmitted sequence would be the total number of pixels in the image, which would be N x N for a square NxN image.

I hope this helps! Keep exploring Shannon's theory and its applications in information theory. Good luck!
 

1. What is the Shannon formula for calculating simple uncertainty?

The Shannon formula, also known as Shannon entropy, is a mathematical formula used to calculate the amount of uncertainty or information contained in a set of data. It is represented as H = -Σp(x)log p(x), where p(x) is the probability of a specific event occurring.

2. How is Shannon's formula used in the field of information theory?

Shannon's formula is a fundamental concept in information theory, which studies the quantification, storage, and communication of information. The formula is used to measure the amount of uncertainty in a system, which is essential in understanding the efficiency of data compression and communication systems.

3. What is the significance of Shannon's formula in data analysis?

In data analysis, Shannon's formula is used to measure the amount of uncertainty or randomness in a dataset. This information can then be used to make predictions and identify patterns in the data. It is also used in data compression techniques to reduce the amount of data needed to represent information without losing important details.

4. Can Shannon's formula be applied to any type of data?

Yes, Shannon's formula can be applied to any type of data, including text, images, and audio. However, the formula is most commonly used in discrete and digital data, where the probability of each event can be easily calculated.

5. How does the Shannon formula relate to other measures of uncertainty, such as variance and standard deviation?

The Shannon formula measures uncertainty in terms of the amount of information contained in a system, whereas measures like variance and standard deviation measure uncertainty in terms of the spread or variability of a dataset. However, there is a mathematical relationship between Shannon's formula and these other measures, and they can all be used to gain a better understanding of a dataset.

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