8080 8085 Assembly Language Programming by Intel Corporation

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N ' j Hi M&1 i '0 The histogram can be used to efficiently calculate the mean and standard deviation of very large data sets. This is especially important for images, which can contain millions of samples. The histogram groups samples Chapter 2- Statistics, Probability and Noise 21 together that have the same value. This allows the statistics to be calculated by working with a few groups, rather than a large number of individual samples. Using this approach, the mean and standard deviation are calculated from the histogram by the equations: EQUATION 2-6 Calculation of the mean from the histogram.

In these cases, the standard deviation is not important in itself, but only in comparison to the mean. This gives rise to the term: signal-to-noise ratio (SNR), which is equal to the mean divided by the standard deviation. Another term is also used, the coefficient of variation (CV). This is defined as the standard deviation divided by the mean, multiplied by 100 percent. For example, a signal (or other group of measure values) with a CV of 2%, has an SNR of 50. Better data means a higher value for the SNR and a lower value for the CV.

2-2, but with less roundoff noise and greater computational efficiency. The signal is expressed in terms of three accumulated parameters: N, the total number of samples; sum, the sum of these samples; and sum of squares, the sum of the squares of the samples. The mean and standard deviation are then calculated from these three accumulated parameters. F 2 ' 1 N& 1 j N&1 i' 0 2 xi & j xi N&1 1 N 2 i '0 or using a simpler notation, F2 ' 1 N& 1 sum of squares & sum 2 N While moving through the signal, a running tally is kept of three parameters: (1) the number of samples already processed, (2) the sum of these samples, and (3) the sum of the squares of the samples (that is, square the value of each sample and add the result to the accumulated value).

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